The tribe unmourned always refers to the sixth house as they were destroyed and forcibly reabsorbed into other houses hence the title. It's definitely a reflection of bitterness Dagoth had to both the great houses and the tribunal.
Keep in mind that those five houses were also screwing over the Dwemer, as they had a treaty at the time. My memory might be foggy on this, but I believe that's why they decided to activate the Numidium when they did, because of the way the Battle of Red Mountain was going. Of course, the "Tribe Unmourned" could also be the Chimer, since Azura changed them in to Dunmer at this time too.
Dagoth was betrayed, but so was Nerevar by Almalexia, Vivec and Sotha Sil. They acquired their divinity from Lorkhan's Heart.
There's a bit of lore differences on the subject of Red Mountain, which is most likely Bethesda being fast and loose with their lore, or it could be "unreliable narrator". There's also the fact that Vivec, Almalexia, and Sotha Sil lied their asses off about what happened on Red Mountain which is evident by the visages of Nerevar all over Morrowind. They were basically gods, but allowed the Nerevar mythos to continue and even embraced it. About the only thing we know for sure is that the Chimer/Dunmer were going to screw over the Dwemer and the Five Houses screwed over Nevevar and Dagoth Ur, then covered it all up.