If I watch a movie or a TV show on Apple TV and then pause it with the physical or virtual distance application, then pressing the "Apple TV Paused Playing" icon in Homekit does not play the currently paused movie, but starts playing at random. song on the same Apple TV. He's angry. I don't just understand Apple's thinking about this.
Pressing the button during movie playback causes it to enter a non-responsive mode that will not return until it kills the application and restarts it.
Long press of the button displays the remote as expected and seems to work fine.