The way I interpret it is that you can reveal it at (1), (2), (3), (5), or at the end of any given action. Once an action is declared, you cannot reveal Turn to Stone until the action is over. So when your opponent casts an attack spell, all 3 steps of casting a spell and all 8 steps of performing an attack are counted as a single action. You could not reveal Turn to Stone between any of these 11 steps. However, you could reveal Turn to Stone between two distinct actions, such as between a move and an attack, or between a first move and a second move action.
Practically speaking, it's pretty common to see people start to move a card without actually flipping the action marker (technically illegal, but they intend to flip the marker at the end of their move). In this case it would be perfectly legitimate to flip Turn to Stone and prevent the action. Formally speaking, he should have flipped the activation marker first, which would have given you the chance to flip Turn to Stone BEFORE he had the chance to move anywhere.
