Unwanted File Timestamp Updates

TBH, I can't tell you for sure.

Every double click on a file in the main File List of Mp3tag automatically save it.
Please also check your Tags options:
image

Every time I run Robocopy I have to copy thousands of files, so it doesn't really matter, if some more "untouched" files will be transferred.
The copy process runs in background, I can do something else in the meantime.

Maybe this question/answer (do not be confused by the title) can help you too: