Interesting. Is there a chance they aren't actually using the scroll bar in the first place though. When I enter and just leave the scroll bar untouched, it scrolls just fine for me. However, if I scroll up, I get the same issue you described.
I am not getting that issue on other wikis so right now the custom JS remains the primary suspect. Also, while the auto-scroll "wasn't working", I noticed that the scroll bar jitters up and down a bit each time a user posts. I am thinking somewhere in the JS, there might be some snippet that is re-scrolling up (as opposed to the auto-scroll not working).
Unfortunately, it is a bit hard to confirm for sure as the chat does not allow disabling of JS via the URL like most pages do. Therefore, I can't test chat with JS disabled to see if the issue still exists.