We don't know yet, but:
In the http://imperial-library.info/content/pocket-guide-empire-first-edition-aldmeri-dominion, an Imperial scholar states that the history of the First Aldmeri Dominion begins in year 830 of the Second Era. This is apparently a different Dominion to the one portrayed in ESO, but much closer chronologically to ESO's dominion than Skyrim's one.
... the Aldmeri Dominion has its origins in CE830, when the heirs of the Camoran Dynasty began to fight over the Valenwood throne. When a faction of the Bosmer (Wood Elves) made overtures of peace to their longtime enemies in West Cyrodiil - territorial concessions in return for Colovian support for the faction's claimant - the Altmer (High Elves) of Summerset invaded the Valenwood Nations. Citing a stewardship clause in a treaty from a thousand years before, the High Elves quickly established a provisional government, the Thalmor, on behalf of their own claimant, Camoran Anaxemes, whose bloodline had struck the pact with the Aldmeri Council in the first place.
So at this time, the Thalmor was a provisional government of Valenwood established by the Altmer. Either this expanded to encompass the whole of the Dominion at the time of Skyrim, or the name refers to a different governmental body. In any case, we don't have records of a "Thalmor" of any sort existing before this time. So it's possible that no Thalmor exists in ESO's Dominion.
My own theory (nothing to back it up yet) is that the Thalmor exists as a ruling body in ESO, but has lost a significant amount of power to Queen Ayrenn - this partially explains why her motives seem very different to Altmer described in the First Pocket Guide and displayed in Skyrim.