I just signed up to try Apple Arcade (love it so far) but noticed that when I install a game on the Apple TV 4K (which I generally use) the same games are installed on the Apple TV (Gen 4) that is in another room. Both have Automatic Downloads for Apps turned off. But from what I have read it has something to do with the Home Kit app on my iPhone – which I had to put near the two Apple TVs after the last update. It has something do do with having the same "home screen" on both Apple TVs, but I don't see any setting – either on the Apple TVs or in the Home App on the iPhone – to turn this option off.
Anyone have any ideas?