Er, Nerevar is Indoril Nerevar...of House Indoril. And all the Great Houses are descendants of the ancient Ashlander tribes, right? So, I'm pretty sure none arose during the time of the Tribunal.
So why is House Dagoth known as the "House unmourned?".
EDIT: The
origins of the Houses were formed when Boethiah and Mephala decided to have some fun with the Dunmer. Same with the Morag Tong. Paws's point is the right, specifically speaking.
I know Nerevar's link to House Indoril. I simply think, by the events of Morrowind it is a corruption of what it once was. Taken over/inherited, and used by Almalexia and the Ordinators for thousands of years. Almalexia was his wife, too. Some would argue that is was corrupted that way. Probably so, really. As such, it lost it's place in the prophecy that the Nerevarine had to fit into.
But that's simply apologetics.