So there’s no setting in usermin to do this?
Well, I’ll tell you what. I’m continually surprised at the breadth of features that are stored within the bowels of Webmin, Virtualmin, and Usermin. I’ve been using it for years, and continue to find new things I never knew existed.
So, maybe there’s some little known feature somewhere that your user managed to discover, one that I’ve never run across. It’s totally possible 
But, if it exists, it’s not on by default, someone would have had to enable it.
Also, I just looked through all the Usermin options I could find that an email use would have access to, and I didn’t see anything related to auto-deleting emails from an inbox.
So, my suspicion is still with the email client 
Also, you can look in the mail logs to determine what’s deleting messages. Anytime an email is deleted, it’ll show up as the user logs out. For example, if a user logs in via POP and deletes an email, there’d be an entry like this:
dovecot: POP3(user@example.com): Disconnected: Logged out top=0/0, retr=0/0, del=1/361, size=43657036
You may be able to use that to determine what is causing the emails to be deleted, and when it’s happening.
-Eric