This is from my own testing using Blizzard’s combat logging system.
- Starting Auto Shot while standing still: the shot fired 0.55–0.60 s after aiming began.
- Stopping after running: the shot fired 0.67–0.93 s after you stopped, so noticeably longer.
- Most likely Why: this is the game’s built-in Auto Shot aim time (about 0.5 s) plus latency. After moving, the game also needs a moment to register that you’ve stopped.
Not sure if Blizz is going to be able to fix it.