When manually updating tags and saving, Picard will update the file modify timestamps even though the Preserve timestamps of tagged files option is checked in Options.

Example:
1. Go to Options-->Tags and Check Preserve timestamps of tagged files.
2. Move a folder of MP3s into the middle pane and cluster them.
3. Manually change the Title of one of the MP3s
4. Click the Save button.
5. All of the timestamps of all of the clustered files now have an updated timestamp.