I asked a similar question some time ago, and it seems shifts that are placed on the same tile and are triggered simultaneously (same collision mask) generally produce unexpected results when multiple flags and other properties are toggled (I think this applies to vanilla KS as well, though). The solution is to make one of the shifts timed, even if it's just a very small delay. E.g:
ShiftTime(A)=1. Note that this works correctly with two shifts,
but not with three, even if different delay values are set for each timed shift.
If all else fails, try making duplicates of that screen (each one with up to two flag-toggling shifts, and a third one just for the screen transition) and keep shifting Juni through those duplicate rooms until all required properties are set.
Edit: I just tried the demo level you attached. The character-changing shift works as expected if Shift A is timed and both Shift A and B are set to trigger in the same way (both manually or both on touch). However, it seems the workaround is not valid if one of the shifts is triggered on touch and the other one isn't.