The Thalmor claim they saved the Summerset Isles, but thats just it they claim it. The implication from The Rising Threat Volume II is they infact did nothing. When the Crisis ended they told everyone they saved Mer by working deep and subtle magic. From what I see they simply stole credit from Martin Septim. The Thalmor's return to power(after the fall of the first Aldmer Dominion) Occured after the Oblivion Crisis.
I believe that it makes more sense that the Thalmor were in fact the group that closed Oblivion gates in the Summerset Isle, than to believe that the gates were left open to destroy the land until Martin closed them all for good. Books in Skyrim, aside from ones such as Rising Threat that are anti-Thalmor, state that during the Oblivion Crisis that Thalmor rose to power due to the prestige they gained by closing Oblivion gates and protecting the land. The Skyrim Wiki even states this about the Thalmor: "They were the group of warriors that closed the Oblivion Gates in the elven lands." This description is probably derived from the books in game.
So just to clarify, the Thalmor did close Oblivion gates in order to rise to power during this time.