When did Dalmasca fall?

[Cilia]

Dalmasca / Rabanastre was one of (if not) the first conquests of the Garlean Empire. It was taken about 50 years ago.

If you're wondering about the destroyed capital Rabanastre as seen in the first Return to Ivalice raid, that happened when the city-state rebelled against the Empire shortly after Doma and Ala Mhigo's successful bids for freedom in an effort to do the same. Without Zenos' lax attitude holding it back and in a show of force to discourage further rebellion, the Empire came down hard on the city. (Ironically this was detrimental in the long run, as without Rabanastre to serve as a refueling center the Empire's range in the region is now limited.)