Hello,

For the test, I added a text element to his site, and it became visible only in the logged-in state. Screenshots:
Logged – visible https://monosnap.com/file/ZxB4N7UKXet7oVTakMAYDlZf2k6Dui
Unlogged – invisible or nothing changed (because of cache) https://monosnap.com/file/YSpN3IvTR192vkn9Jn1NIAhN4OnRSH

This means that his site is under the influence of some cache. It can be both a plugin or a cache on hosting. If the plugin has already been discussed, then let him check the cache on the hosting. Our theme cannot influence this.

Best Regards.