Each team’s offense uses their own footballs. They are kept separate, and there are also separate balls for the kicking plays (punts, kickoffs, free kicks, field goals, extra points).
Didn’t know that but in thinking about that, doesn’t that seem like a goofy rule? I mean in baseball, MLB/umpires provide the baseballs during the game. I don’t see a good reason for a rule like that which potentially allows stuff like this to happen.