No, they never said that. You are thinking of a gameinformer article that was referencing the 3rd edition of the Pocket Guide to the Empire. Falinesti didn't stop moving until the 3rd era. For all we know, Falinesti might not even be in the game at launch.
I'm gonna have to go reread that article. They honestly did a poor show with that article; there were a lot of assumptions made based on misinterpretations and bad info, that they then presented like it was the word of the devs. This may indeed be a case of that that I didn't catch.
Edit: from the gameinformer profile of the aldmeri dominion:
"
Valenwood is located in the southwestern region of the Tamriel. Home to the Wood Elves, Valenwood is covered by wide swaths of uninhabited forest. Swamplands and tropical rain forests dominate Valenwood’s coasts, but the nation’s most unique features are a few of its cities which are housed in giant, migratory trees. Valenwood’s capitol Falinesti, actually used to migrate south in the winter, but the tree containing the city has recently stopped walking."
we shall see....