I recently proposed that the fission of Proto-Uralic *ä and *e into more open and more close vowels in Samic, depending on the following second-syllable vowels (“stem type”), should be dated already to the dialectal West Uralic era, given that similar developments appear also in their closest relatives: the Finnic and Mordvinic languages. This diverges in a couple of ways from the views in the main handbooks on the historical development of Samic, i.e. Korhonen (1981): Johdatus lapin kielen historiaan and Sammallahti (1998): The Saami Languages: An Introduction.
One basic disagreement is over absolute chronology. While both Korhonen and Sammallahti (henceforth: K & S) agree that at least the merger of the stem types *e-ə and *i-ə  should indeed be dated to the earliest phase of the pre-Proto-Samic era, their treatises begin from the now obsolete “Proto-Finno-Samic”, dated as some half a millennia later, reconstructed with cross-reference mainly to Finnic, and usually also located some 1000 km more westerly (in the Gulf of Finland area) than my reference point in common West Uralic (around the upper reaches of the Volga). 
Another however concerns the overall relative chronology. K & S present the historical phonology of Samic in a highly tiered fashion that makes for some very attractive charts and graphics, with roughly four distinct periods of development:
- an early phase (K’s “kantalapin I vaihe“, S’s “Pre-Saamic” and “Proto-Saamic 2“) with the loss of several inherited vowel contrasts, and the splitting of this smaller pre-Samic vowel system into several allophones, depending on stem type;
- a complete revamp of the vowel length system (K’s “kantalapin II vaihe“, S’s “Proto-Saamic 3” in parts), depending on earlier vowel qualities;
- a restructuring of the system of unstressed vowels (K’s “kantalapin III vaihe“, S’s “Proto-Saamic 3” in parts as well as “Proto-Saamic 4“)
- late phonetic shifts in the sound values of several stressed vowels (K’s “kantalapin IV vaihe“, S’s “Proto-Saamic 5“).
As I have mentioned in an exchange in the comments section, I am however skeptical of the historical reality of this model. It strikes me as unnaturalistically neat altogether. Only a few of the changes can be explicitly shown to have been in the presented order in relative chronology, and probably most of the distinct “phases” here should be meshed together. Others might even be post-Proto-Samic entirely (though that will be another topic).
In particular I do not think that all Proto-Samic umlaut developments should be considered equally early. The Samic languages are some of the most “umlaut-rich” languages within Uralic, and the individual languages have continued to innovate new changes of this type pretty much as soon as new features arise among the unstressed vowel system. In this context it seems entirely implausible to me that at one point the pre-Proto-Samic speakers would have collectively decided “ok, that’s enough for now, let’s call a 500-year moratorium on umlauts”.
More specifically, while I think that developments *ä-ä > *ȧ-ȧ (> PS *ā-ē) versus *ä-ə > *e-ə (> PS *ē-ë) might be even earlier than has been previously suspected, by contrast I think that the a-umlaut of inherited *e and *o (e.g. PU *pesä >> PS *peasē ‘nest’; PU *kota >> PS *koatē ‘tent, teepee’) must be instead dated to a somewhat later Proto-Samic phase. This is due to some exception cases that appear to be explainable by them having been subject to both umlauts.
It’s been observed already since the earliest reconstruction work on Uralic vocalism that PS *ea fairly often turns up in the Samic languages as a reflex of earlier *ä. Explanations for these cases have varied quite a bit, from considering this the regular reflex of the stem type *ä-ä (this was the opinion of Wolfgang Steinitz), to dismissing all instances as irregular or “sporadic” (thus K & S). Neither extreme is satisfying though, and it would be desirable to identify some conditions for the development. Dating the umlauts of *ä and *e into two different chronological stages seems to offer a lead on this.
If we assume that the pre-Samic dialect of late West Uralic — I will call it “pre-Samic” or “preS” for short — had already raised *ä-ə to *e-ə, as in words like the following:
- PU *jäŋə [jɛŋə] > preS *jeŋə > PS *jēŋë ‘ice’
- PU *kälə [kɛlə] > preS *kelə > PS *kēlë ‘tongue’
- PU *mälkə [mɛlkə] > preS *melkə > PS *mēlkë ‘breast’
— then at this point, a derivational process turning one of these *ə-stem words into an *ä-stem word would allow it to be later subject to a-umlaut just as inherited *e is, yielding PS *ea. There appear to be some clear examples that involve the syncope of *-ə- upon the addition of a derivational suffix: PU *CäCə > preS *CeCə → *CeCə-Cä > *CeCCä > PS *CeaCCē. Some other examples involve a derivational process that leads to a pre-Samic *o-stem (which similarly trigger a-umlaut): preS *CeCə → *CeC-o > PS *CeaCō. 
This mechanism appears to explain a reasonable number of the cases of PU *ä yielding PS *ea. Thus far, I have identified seven possible front-vocalic cases (including one somewhat speculative new etymological proposal):
- *keaćō ‘medium-sized whitefish’ (only in Lule Sami: getjuk) < preS *keć-o
← *kećə < PU *käśə(ŋ)
Cf. Mansi *kääsəŋ, Hungarian keszeg ‘bream’, which both indicate earlier *ä. (Finnish keso ‘white bream’ has also been considered cognate, but is better derived from kesä ‘summer’.)
- *leapō- (Lule Sami lehpagis ‘nice’, Old Swedish Sami leppotet) < preS *lep-o-
← *le(p)pə < PU *lä(p)pə
Cf. Moksha /ľäpä/ ‘weak’, Mari *lewə ‘warm, mild (of weather)’, Khanty *leepət ‘weak’, which indicate *ä. Finnic *leppedä ‘balmy’ again looks like the odd member out in the cognate set. The similar *leepedä ‘mild’ could be instead compared here just about as easily. 
- *meanō- ‘to become evasive’ < preS *men-o-
← *menə- < PU *mänə-
Cf. Mordvinic *mäńə- ‘to dodge, to get free’, Komi /mɨn-/ ‘to get free’, Hungarian mentes ‘free’, which indicate *ä. The verb *mänə- ‘to get free’ is probably ultimately somehow related to *menə- ‘to go’, but the cognates suggest the two having been distinct already at the PU level. (I additionally wonder if contamination from the former could perhaps explain the irregular vowel in Savonian/Karelian mäne- ‘to go’.)
- *peajō- ‘to shine’ < preS *pej-o-
- *peajvē ‘day’ < preS *pejwä < *pejə-wä
both ← *pejə < PU *päjə ‘bright, shining, etc.’
The bare root does not appear to unambiguously survive anywhere (perhaps in Komi /bi/ ‘fire’?), but numerous other derivatives generally indicate *ä, e.g. Finnic *päivä ‘day, sun’, Hungarian fehér ‘white’.
- *pealkē ‘thumb’ < preS *pelkä < *peləkkä < PU *pälə-kkä
Cf. Mordvinic *päĺka, where the unvoiced cluster *ĺk must be secondary (PU *lk would have yielded **ĺg). Komi /pel ~ pev/ also suggests *ä. The underived root could be identified with *pälə ‘side’, as has been proposed by Janhunen. The messy Finnic words for ‘thumb’, often included here, mostly point to PF *peikala or *peikoi; and they probably need to be kept separate (at best some kind of secondary contamination of the original Uralic word with some other source could be involved).
- *veakkē ‘help’ < preS *wekkä < *wekə-(k)kä
Formally, this might be a derivative of PU *wäkə ‘power’ > preS *wekə (> PS *vēkë ‘people’). A semantic intermediate ‘activity with several people, work bee’ could be involved.
It is however necessary to also assume similar but even earlier syncope in some other old derivatives, which do show regular a-umlaut in Samic.
- *ńālmē ‘tongue’ < *ńälmä (~ Hungarian nyelv ‘tongue, language’ etc.) ← PU *ńälə- ‘to swallow’
- *ńālkē ‘tasty’ < *ńälkä ← id.
- *pāŋkē ‘reindeer’s headgear’ < *päŋkä ← PU *päŋə ‘head’
The first of these words has a very wide distribution, and the bisyllabic form *ńälmä could perhaps be assumed already for PU… though this would get in the way of a partial rule for *m-lenition in Hungarian that I have sketched some years ago.
I can also think of a slightly different mechanism to account for one of the remaining high-profile examples of *ä >> *ea. This is *pealē ‘side; half’. The polysemic meaning suggests that this may have come about as a blend of two originally distinct PU words: the above-mentioned *pälə ‘side’ (> Finnic *peeli, Mordvinic *päľ, Mari *pel), and the evidently closely related but distinct *pälä ‘half’ (> Finnic *pooli, Mordvinic *päľə, Mari *pelə).
The two words also seem to merge in Ugric: compare Hungarian fél : fele- ‘side; half’; Mansi *pääl ‘side; half’; Khanty *peeɭək ‘side; half’. But while this development can be simply due to the loss/reduction of 2nd-syllable vowels, the Samic development would require assuming contamination: the stem vowel seems to continue preS *pȧlȧ ‘half’, while the *e-type 1st syllable vowel seems to continue preS *pelə ‘side’. The two would led to the creation of a preS “compromise” form *pelä, from which then regularly > PS *pealē.
Worth noting is that in the case of ‘day’, a similar exception development is also found in Finnic. PF *päivä ‘day, sun’ (and not **paivi) has likewise escaped the early lowering/backing of *ä-ä, perhaps for the same reasons too: contraction from *päjə-wä taking place only after the a-umlaut of primary *ä-ä.
This pattern seems to extend further: among the remaining cases with *ä > PS *ea, Finnic cognates usually have *ä-ä as well. At least five cases can be identified that have correspondences in the more eastern Uralic languages:
- ‘lichen’: PS *jeakēlē ~ PF *jäkälä (~ Permic)
- ‘paw’: PS *keapēlē ~ PF *käpälä (probably related to *käppä ‘paw’ > Finnic, Mordvinic)
- ‘bog’: PS *jeaŋkē ~ Fi. jänkä (~ Permic, Mansi, Khanty)
- ‘flap, cover’: PS *leappē ~ PF *läppä (~ Mari, Permic, Hung., Mansi)
- ‘smoke hole’: PS *reappēnē ~ PF *räppänä (~ Permic)
While this same correspondence is also common enough in loanwords (PS *(h)earkē ← PF *härkä ‘bull’; PS *kearnē ← PF *kärnä ‘crust’; both originally from Baltic), and this approach has in the past been applied to ‘bog’ (S → Fi) and ‘paw’, ‘flap’ (F → S) as well, nothing seems to outright require considering these words later than the pre-Samic / pre-Finnic period. If *ä-ä [ɛ-a] had in both groups been lowered to *ȧ-ȧ [a-a] by then, new lexical innovations of the time could reintroduce also a new, secondary *ɛ-ä in pre-Finnic (*jɛkälä ‘lichen’, etc.); while in pre-Samic, only *e-ä would have been available.
Conveniently enough, there is also one word of this type for which early loaning in the West Uralic period is assured: PS *keavrē ~ PF *käkrä ‘bent’, which probably derives from Indo-Iranian *čakra- ‘wheel’ (or from a slightly earlier *ḱɛkra-). 
To be sure, I still generally hold that if two competing etymologies are available for a word, then all other things being equal, the more recent explanation should be preferred. But this is only a probabilistic rule-of-thumb. So while several of the words here (and also many of the more numerous similar cases yet that are restricted to Samic & Finnic) probably have indeed been loaned between Finnic and Samic at a later date, I would not rule out the possibility of some of them still going back to different parallel preS and preF sound substitutions in the late West Uralic era.
For now I’m still sketching out the situation with back vowels. In particular it’s not clear to me how the raising PU *ë-ə and *aj(C)ə > preS *a-ə > PS *ō-ë should be dated: this is attested from numerous Germanic loanwords, and thus could be newer than *ä-ə > *e-ə. It may well be the same change as preS *a-a > PS *ō-ē (likewise attested from Germanic loanwords); and thus not triggered by stem vowels at all.
 In their view the result of this merger would not have been quite [i], but a near-close vowel they mark as *ḙ. I would suggest the sound value [ɪ] for this (similarly [ʊ] for their *o̭), reflecting the common tendency of close short vowels to reduce and centralize. Initially this probably would not have had any phonological signifigance though, so I will continue to use *i and *u for the early pre-Samic and early pre-Mordvinic era.
 “Common” rather than “proto”: while West Uralic at least seems like a defensible subgrouping to me (unlike its traditionally assumed kin like “Proto-Finno-Volgaic”, “Proto-Finno-Permic”, etc.), the common innovations are not many, and it remains effectively only a dialect of Proto-Uralic itself. This being the case, an accurate picture of West Uralic can only be gained by starting from Proto-Uralic and “reconstructing upwards”, not by presuming the existence of the group and attempting to compare Samic/Finnic/Mordvinic in isolation (a method that has traditionally generated rather Finnocentric models, further muddled by conflicting evidence from areal later-diffused vocabulary). It would also be premature to rule out entirely the possibility of WU being an “areal-genetic” group of dialects after all, since non-exact parallels for a few of the characteristic innovations (e.g. *ë- > *a, *åĆ > *aĆ, *-d₂- > *-d₁-) can be found in Mari, Permic and even Hungarian as well.
 It does not seem clear to me if these cases should be assumed to involve the suffixation of a consonantal suffix such as *-w and a later development *-əw > *-o, or simply the addition of *-o as a suffixal element right away, but this does not really affect their validity. If the former though, then this has some implications for the history of the PS stem type *ā-ō; they could not descend from *ä-o at the West Uralic level, but would have to go back to preS *ȧ-ȧ < PU *ä-ä, with the labial suffix only as an incidental addition.
 The irregular vowel correspondences in the Finnic words could perhaps be accounted for by assuming contamination from the Germanic loanword *leevä ‘slight; temperate’. This is one of the very old Germanic loans in Finnic that shows *ē → *ee. While both sides appear to point to a mid vowel [eː], I believe this is illusory. PIE *e was probably closer to [ɛ], and the eventual lowering and backing of *ē to *ā in Northwest Germanic suggests that even an intermediate [æː] existed at one point; as is also shown by the existence of a couple of loanwords in Finnic that have *ē → *ä (e.g. PGmc *wēgaz ‘lever, scales’ → PF *väkä ‘hook’). Pre-PGmc *klēwas ‘lukewarm’ was thus probably loaned as pre-Finnic *lääwä, later raised to PF *leevä together with inherited words like PU *lämə > preF *läämi > PF *leemi ‘broth’. At this period it could be assumed that pre-F *läppətä ‘mild’ was adjusted to *lääpətä, on the model of *lääwä; with later raising then giving PF *leepedä. — Even slightly earlier *leeppedä could perhaps be assumed, with PF *leepedä and *leppedä representing two ways of naturalizing the overheavy syllable structure.
 Another highly similar word family exists as well: PF *käprä ‘rolled up’; PS *kēpr-ë- ~ PF *käpr-i-stä- ‘to roll up’. As has been proposed by Katz, in principle this might represent an earlier parallel loan with PIE *kʷ still retained on the loangiving side, substituted by pre-S / pre-F *p. Dating *l > *r in Indo-Iranian as already this early seems unlikely however, and I suppose a more probable explanation would be that this is Uralic-internal descriptive variation. Note also a number of obviously secondary formations in Finnish such as käkkyrä, käppyrä ‘curved thing’.