In my experience, the only way to 'force' backup is to make it so that all of your user's data is stored on a network drive either through file sharing or a NAS. Make them very aware that any local data on their computers is completely unprotected, and any loss of data is their own fault.
I even had to sign an agreement once acknowledging that I fully understood this!
*****Also, make sure that Local Mailboxes are never used!!! I had someone completely loose their work emails due to moving all their IMAP mail into local mailboxes, as it was the default action when asked to make a local one. No idea if it's possible to grey out local ones, but this completely threw me having not thought of it!
I have never used it, but you can also use time machine on all client computers (as a whole, not per user I believe for ease of use). This would seem the most effective, but I guess would be a drain on your existing TB's of server storage...? Good luck!