Yes, your ticket or AP must be valid for the dates that you are getting FP+ reservations. I learned this the hard way and my lesson learned is something for AP holders to take note of.
I am DVC and a premium AP holder. My next vacation is 13 days long and my AP expires 3/4 way through the trip... therefore I cannot make FP+ reservations for the last 1/4 of my stay.
I thought, no problem, I will just renew my AP now and book the rest of my FP+ reservations. Turns out that even if I purchase now my renewed pass is not valid until I use it at a park gate which will leave me scrounging for the leftover FP+'s.
Had I known the rules 11 months ago when I booked I would have made my reservation a couple of weeks earlier or later.