Yeah, it's the losing coach who is supposed to make the first move.
However, while I heard (non UConn) fans behind me declaring it was over with about 4 minutes to go, I will never forget watching a Duke - MD men's game, when I lived in MD and followed the team. The Turtles had a ten point lead with one minute to go, and lost, so I never consider a game over until we get to the one minute mark with more than a ten point lead.
I don't begrudge any coach who is still trying to win with 90 seconds and 15 points, it isn't over then. I do get annoyed when there are 20 seconds and a dozen points, and the coach doesn't call them off. I don't recall exactly when Muffett called them off, but I don't recall thinking it was far off my personal towel throw in mark.
I'll also note it is on the coach, if a player is still pressing with ten seconds left, it is on the coach to call off the dogs, not the player.