Access based on Classification not working in Web Client

We're currently on 9.2.

A large number of our classifications have Default Record Access for view/update/modify/contribute set as Not Reference, records based on Owner.  This works fine in the full client.

In the web client, anytime someone uses one of those classifications, it leaves the view/update/modify/contribute as Unrestricted and does not pick up the owner.  

Any thoughts on why this may be happening?