ReplayMod 2.5.1 (1.16.4)
When auto record is ON and you do record on server, the pop-up with replay saving always show 0% until process is done. But if you turn auto record OFF and manually click Start/Stop recording when on server, then everything works as intended.

Reproduce:

• Join the server (auto record will start)
• Leave the server

There isn't actually any difference between manual and auto recording in this respect, it's just that with auto-recording all the parts that do have a progress (namely cutting the replay into parts) are skipped and only the first step (creating the mcpr archive from the individual files) is left.
So, in that sense, this is working as expected.

It shouldn't be too difficult to add some indication of progress for that first (and sometimes only) step as well, so I'm labeling this as an enhancement.