I like the idea of an Ayleid sleeper cell that knew the only way to counter the Empire's strength was to orchestrate an Oblivion Crisis and then usurp power from Summerset lol. Gives the TES universe a new political spin on things.
It's funny that you should say that because that is exactly the case in my headcanon. There is one surviving ayleid (from before the downfall) who has "returned" for lack of a better world; whether he was in stasis etc etc during all this time I haven't decided but he has certainly been absent for the second and most of the third ages. This ayleid is the pulling all the strings, encouraging Mankar to initiate the Oblivion Crisis in order to cause the uprising of the Thalmor who he has secretly been funding. As of the fourth era he isn't the official leader of the Thalmor, he is the unseen power behind the throne. He intends to unmake the world so he can bring all his people, who were unjustly massacred by filthy animals, back to life. There are many more details and his web spins much deeper into Tamriel than I have said but that is for another topic and another time.
As for the original topic, I personally do not believe that the Thalmor is an ayleid inspired movement. I have no doubt that there are ayleid-blooded altmer in the Thalmor but overall I do not believe they are motivated by their heritage in any way. There is nothing except for the discussed source to hint that the ayleids are in any way involved in the Thalmor's plot. I would also like to raise the question as to whether we can even treat this source as a credible one since it is, afterall, written in character. The author, Nu-Mantia, is entirely unknown to us as are his ties to the Thalmor/Altmer and the source of his conspiracy theories. He is no doubt wrong about some of the things he writes in his letters. If MK wanted to give us inerrant information he wouldn't have done so in character.
As others have said there are multiple candidates that could fit this ayleid threat instead of the Thalmor. Mankar, Umaril and even Umbacano are the most likely candidates. Umaril's heritage is unquestionable. Mankar's, I believe, is capable of being traced back to the ayleids who interbred with the Bosmer. Umbacano's heritage is unknown but at the very least he believes that he is worthy of being called an ayleid.