I took judo as a kid and we drilled falls constantly. I've also both studied and/or taught various MA for years. While muscle memory in a fight can take years to learn, the fall techniques we drilled were quick to become automatic. In fact, after the first month or so I can't recall ever "thinking" about how to fall. It just became instinctual. I believe that those instincts were a big reason why I never broke any bones despite being a fairly reckless kid.
In terms of football applicability, I feel that the one fall technique that is most applicable will be automatically tucking your chin so your head doesn't smack the turf. In my experience that's something that becomes automatic pretty quickly. I have no trouble believing that Tua could have that muscle memory ingrained in a few months of training. It would depend on the training of course, but judo and jujitsu classes I've seen tend to do those fall drills daily.