Et al,

From the data I've gathered here on several posts and on reddit, the average delay is between 5-7 seconds. A D&D Turn is 6 seconds and this is built into the game at its foundation. I believe these delays have something to do with the turn-based flag being turned on when certain actions occur in real-time. What is turning that flag on I cannot say yet because it is widely inconsistent. For example, on my playthrough when I summon something in real-time (not turn based action) it appears immediately, but sometimes when I unsummon/dismiss it, it requires 6 seconds.

So when swapping to turn-based you're effectively just breaking up real-time into 6 second intervals and everyone goes through initiative including the environment. In real-time, it should all happen simultaneously. What appears to be occurring is in some instances, it's making you wait a 'turn' for a real-time event like a jump or dismissing a summon, and in some turn-based rolls, you're still waiting an extra 6 seconds (like swinging at an enemy and 6 seconds later it tells you if it hit or missed), but the swings before and after that were fine.

Inconsistent bugs are the toughest to track down, but the theory that fits the facts here is that it has something to do with the turn-based 6 second wait being incorrectly flagged for different actions at different times. I'll update on this again when I find something more concrete to point at a root cause.