Keep in mind there are file permissions, folder permissions, and share permissions. If one of them is askew, it may affect their login. Have any users been locked out due to excessive wrong password uses in your scenario?
In another scenario, perhaps the redirect to the server is explicit, instead of implicit. That is, the user’s machine ‘sees’ that it must go directly to the IP address (possibly a private, non-routable address) to access the public folder.
However, the fact they are being ‘logged out’ implies they have violated some rule. Ensure you examine the Event Viewer logs (system and security, particularly) after staging a test logout event.