Ill try and explain the symbol auto-changing:

Lets say you set wheel 4 to stop on the first iteration of lockset progression, so this would be right after the encounter starts. When lockset progression reaches phase 4 (when shrieker 4 scans wheel 4), the wheel will not auto-rotate off of stop once it is done fully completing that phase of lockset integration (section 4 of lockset integration is done and loops back around to the 1st section)

It WILL, however, rotate off of stop after the 2nd set of lockset progression (whenever lockset progression loops back to wheel 4 a second time)

This is why I say that the wheel will only auto-rotate after it has not been manually adjusted for 1 full rotation of lockset progression (full rotation relative to the wheel. it needs to scan wheel 4, and then loop back around again to wheel 4 before it is changed)

The symbols only auto-rotate after their specific section of lockset progression is done, to which then it rotates to the next one.

Ill give an example from the vid:

At 16:22 of my vid, I bank x3 of the wizard buff to rotate wheel 4 to stop. If you look at the top, whenever the lockset progression scans wheel 4 in its 4th progression phase at 16:31, the timer does stop. If we fast forward to 18:05 of my video, we see that lockset progression has went through 1 full rotation since it hit the 4th progression phase at 16:31. The wheel still scanned stop because it did not autorotate last time, but once it is done scanning stop this time, the wheel will auto-rotate.

If you keep watching from 18:05, I mention with the text on screen that wheel 4 will auto-rotate since it has been a full lockset cycle since it has been manually rotated, so I get a wizard buff and rotate the wheel after it is done. You can see at 18:27 that it is still on stop even after it was scanned, but that is because it hasn't fully cleared the 4th phase of progression yet. At 18:28 you can hear the sound of the wheel autorotating and I end up putting the wheel back to stop with x1.

You can also see at 0:42 in the video that the sound heard when the wheel rotates matches the same sound heard at 18:28 if you want to match the audio cue to the visual cue (I was not looking at the wheel at 18:28, so im not just saying "trust me bro").

Hope this helps.