How do I share an Apple TV account on Apple Devices?

We've been successful at sharing an Apple TV account on our Windows PCs, but we're having a difficult time sharing the same account across Apple devices (specifically, another iPhone and an iPad). We've followed the directions on the web, and nothing is working. This is what we've tried:

1. Go to settings on the iPhone that owns the account.
2. Go to the Apple TV app. and sign in Home Sharing as the owner of the account.
3. Repeat on the other iPhone and the iPad.
4. That works for the source iPhone but not for either the destination iPhone or iPad (which are owned by another user). Both of those devices show the destination owner within the app itself.

What gives? Supposedly, we can share the same account across multiple devices in the same household and I don't understand that's the case for Windows but not Apple devices.