Just to avoid confusion, there is no Paramount app available on iMac, you had signed up directly in the Apple TV app (which are called Apple TV channels). So that subscription would have been available in the same app via the Apple TV box.
Hulu does not offer an Apple TV channel, signing up to that service on their website on computer will allow access using the same credentials on the Hulu app on the Apple TV box.
When you use the Paramount Plus app on Apple TV after having subscribed in Apple's app it will not work unless you choose to sign in with provider, which will give the option to select Apple TV app and sign in with your Apple account.
Alternatively, you can sign up directly with Paramount using their app (on Apple TV box or other mobile devices), which it sounds like that is what you have now done. The restore option is for when a user has restarted a subscription with Paramount directly but used their Apple account for billing.