I don't get your logic, and no the Tribunal is older, or at least older then 3000 years.
Anyway if she was around during the time when Dragons ruled Skyrim, when the dragon war was going on, when dragon priests walked around when the Dwemer and the Falmer were around don't you think she would have been a bit more surprised to see all that changed since then?
Notice also how she does not seem at all surprised to see a Dunmer, which she would have to be if she was around back then. 4000 years, 1500 years, 500 years there are problems with nearly each age. Before or even in the first era just seems way more unlikely to me then other ages.