Disregard every other explanation you've heard, this comes straight from the Japanese version of VA. The English translators got it wrong completely.
Basically Epitaph shows him what's fated to happen 10 seconds in the future, and this prediction CANNOT be changed, it is guaranteed to happen. That is unless Diavolo uses King Crimson, which deletes up to 10 seconds of time and whatever happened to him in that time is ignored, but everything else sill happens to everyone else. He can move how he wants in those 10 seconds. So let's say Diavolo sees himself get punched in the prediction and then punch the other guy in the face, he can't escape no matter what so he just deletes the time in which he got punched so it doesn't happen, but because the other guy is not Diavolo he still suffers from the result of being punched. Results from actions that would have occurred in deleted time still occur unless they are results that would have an effect on Diavolo. To everyone else it just seems like teleporting since they move from where they were when KC was activated to the end of the prediction instantaneously. They don't remember how they got there because the time they moved in literally didn't happen. On top of this Diavolo can decide how he would have moved in the erased time whereas everyone else must do what Epitaph predicted. Diavolo uses this to disorient people and get behind them in the perfect position to do his fisting 😳.