You wrote:
Could I ask which booking code your tickets were booked into? If you go to AA.com and look in My Reservations, you should see a column for your itinerary labeled Cabin | Booking Code. I would guess V but just want to be sure.

I write:
Yes, we are booked on V class all the way from LAS-MIA-SJU-PUJ and PUJ-MIA-LAS.

I might add that I too have seen points posted to my Citi statement BEFORE I took the actual flight (I tend to book my vacations at least 3-4 months in advance due to work) but my Global Impact points were charged by a company called Valley Travel out of California (???) Points for this award flight have not "popped up" in my TY account yet but the card was just charged last statement. I have noticed that there is a 1-2 month lag between buying the ticket (having the card charged) and getting the points, the actual flight dates seem to have nothing to do with it.