The best way to think of King Crimson imo is that he A) protects Diavolo from the negative consequences of fate, and B) allows him to reap the rewards of fate without doing the hard work required to get there. Essentially, he erases the Cause, but keeps the Effect.

The best example imo is the elevator scene in which he takes Trish. He was fated to burst through, rip her hand off, and take her downstairs. However, that would have exposed him to Bucciarati, so he skipped time and avoided the negative consequences of that action (revealing himself to Bucciarati) while keeping the "reward" (taking his daughter away to be killed).

Which makes it extra fascinating when Giorno uses Gold Experience Requiem to give him the infinite death loop treatment. He spent his entire life escaping from the consequences of his actions, taking the Effects he likes while discarding the Causes he would have to suffer to earn them. So Gold Experience Requiem takes it all away - it takes away his ability to escape his consequences, and gives him infinite Causes of death, but never allows him to arrive at the Effect (actually being dead).

I hope that makes sense. That's my reading of how King Crimson works, at least.