AppleTV has started randomly playing music from my iPhone music library

Earlier tonight, the screensaver on my AppleTV started, and when it did, songs from my iPhone's music library started playing on top of the screensaver. My phone was on standby in my pocket when this happened (and the "Alway On" display setting is turned off fwiw).

I've had my AppleTV for almost a year, and it's never done this before. I didn't change any settings on either device related to music, screensavers, or otherwise. In fact, I've never even opened the Music app on my AppleTV before tonight. Now I can't get it to stop doing this when the screensaver comes on.

Nowhere on my iPhone does it alert me that music is being played from my device on the AppleTV. The usual home screen widget that shows when something is playing on the AppleTV is also missing.

When I open the Music app on my iPhone (or check the music widget in the control panel), it shows under the Airplay tab that it is set to play thru my iPhone, NOT the AppleTV. It is also showing a different song than what is playing on the TV.

As far as I can tell, there are no related settings I can change on the AppleTV itself.

Again, there is NO INDICATION on my phone that this is happening. How do I stop this insane behavior?