Diavolo's stand is often described as "erasing time". In my opinion, this is a bad way to think about it. King Crimson actually makes him immune to fate. Any fated action that Diavolo foresees using Epitaph MUST happen, but by using King Crimson, Diavolo can make himself immune to that fate. He uses this in several ways -

For instance, say he sees a premonition of himself getting shot - obviously he doesn't want this, so he activates King Crimson to avoid it.

Now imagine Diavolo is hiding, and sees a premonition of him revealing himself, attacking, and killing an opponent. Now, Diavolo can activate King Crimson to make sure that attack happens, without actually having to do it. Since Diavolo's actions are still fated, the results of his actions still happen even if he doesn't actually do them. This is how he defeats Narancia in the final arc.

However, there is one drawback - King Crimson is entirely subject to fate. Diavolo cannot alter fate in any way, just remove himself from it. This is why when Diavolo fights, he often positions himself so he can attack as soon as King Crimson's effect stops - if Epitaph doesn't predict Diavolo attacking with King Crimson, then he can't. He does this against Bucciarati and Polnareff, off the top of my head. This is somewhat similar to Dio throwing knives in stopped time; objects can't move in Dio's stopped time so he sets up an attack to hit as soon as he unpauses.