There is a difference between the Apple TV app, and the Apple TV+ service.
You can install the Apple TV app and not signup for or use the Apple TV+ service, or have/use an Apple account of any kind.
You also do not need to sign up for any Apple subscription through Roku Pay in order to install the Apple TV app.
However, in order to stream content, be it Apple TV+, or rent/buy shows/movies, or add subscriptions for other content, you do need to sign into the ATV app with an AppleID account.
Once you install the Apple TV app, open it and navigate to Settings/Accounts/Sign-in, and use any pre-existing AppleID account, or create a new one if you want.