I like tightening the saddle from both sides. Sort of like the way an english saddle is cinched only mine is western. I put latigos on both sides instead of a latigo on the near side and a off billet on the off side.
I go from side to side tightening and counting the holes so I'm on the same hole on both sides. I think its easier on the horse, but that is just a personal opinion.
I always did the tie off method before I started doing it this way.
I believe either way is proper. Back when I first started riding there were no holes nor buckle stay pin,so you had no choice. That was 40 years ago though
we've come a long way.