Cannot control volume on Apple TV using iPhone

The volume control through the Apple TV Remote app, using the side buttons, is available only for when using an AV receiver that supports volume control over HDMI-CEC. The Apple TV box receives the signal through the home network, then relays that through CEC.

The physical Apple Remote uses IR to send the volume control signal directly to the TV (or receiver); not to the Apple TV box (when the above doesn’t apply). Your iPhone is not able to send an IR signal.

As above, the physical remote works with IR. This allows it to automatically control a TV's volume. When using the remote app it is not possible to use IR as the hardware does not support it, so when you use the buttons on the iPhone it will only work when you have it connected to a receiver that supports HDMI CEC.

The physical Siri remote is designed to work control different TV's volume. It is not the same as trying to use one TV's remote to control another. Your question was regarding using the remote app on your iPhone. That hardware is not capable of sending IR and thus it can only work with HDMI CEC. Volume control via CEC is only supported on receivers, and it will require that the device be connected directly to it.

Yes, as I said it is designed to work with different TV's. This is a user forum, if you want more specifics then you can contact Apple.

It will only be used to control volume over IR with the TV. The other functions are tied to the Apple TV. CEC is built on communication between the TV and Apple TV (i.e. once the remote wakes up the Apple TV it will then allow the connected TV to also turn on and switch to the appropriate input).