iCloud-Sync with multiple user profiles on Apple-TV does not work as expected

With tvOS 17 the use of multiple user profiles on Apple TV (each one with Its Apple-Account) was introduced.

Here’s my current situation: I have two Apple TVs linked to my Apple account, and iCloud Sync for the Infuse app works perfectly between them. At my parents’ house, I set up my old Apple TV using my account but also added my dad’s Apple account, which he primarily uses. However, I noticed that the Infuse app on his Apple TV is syncing with my iCloud account, rather than his, which is what I expected.

Does Infuse recognize separate user accounts on Apple TV for iCloud Sync, or is iCloud Sync limited to one Apple account even when Family Sharing is enabled?

Thanks very much in advance for any guidance!

Who do you have set for the Default User on the various devices?

This may help shed some light on your questions.