TB stores messages in one file per folder by default (mbox format), so every time a message is added or deleted, or the folder syncs with the mail server, the time stamp may change. Even if messages are deleted, the mbox size may not change until the folder is compacted and deleted messages are permanently removed.

To sync mail between devices, the usual approach is to have all accounts set up as IMAP.

Let me make sure you understand.

I have an email, I right click on the email, I select Save Selected Message / EML Format. The email is saved.

EML file extensions are associated with TB. Something is updating the timestamp on these .eml files. I am assuming it is TB since these .eml files are the only ones doing this.

I may have resolved the problem, only time will tell. I found a problem on Microsoft. They had the same complaint. The suggestion was to turn off indexing on .eml files. I did that and it appears the problem stopped.

I will let you know.

Once you save messages as eml files, they are stored outside of the TB profile folder and are not affected by TB. Only an external program or process could be affecting the timestamp, which seems to be what you have found.