Adding/removing content to customs tags and/or adding/removing a cover using "or link to the original picture file" modify the size/date of the mp3 file when only one file was selected.
If two or more files were selected, musicbee updates its database without altering the mp3 files.
Configuration
Tags(1) "don't update file modification time when saving tags" is unchecked
Tags(1) all custom tags are set to "Save to MusicBee database only"
MusicBee 3.5.8338 (4gb patched)
Thanks for reading