I bought tickets mid-month and got the credit two weeks later at the end of the billing cycle, as Mia noted above. The CSR with whom I had spoken earlier said it could take longer, but it didn't.
It all makes me laugh, in a way. Three tickets to BWI for $450 (thank you Spirit); $250 of that back with the airline credit (thank you Prestige); and no first-year annual fee at all (thank you Citi private bank).
Plus effectively 5% back on top of all that after taking into account triple points and the annual "relationship bonus."
As I said, I really do have to laugh. Even though the travel gods will nail me next time, surely, it's nice to win one every once in while.