Daughter's Homepod music showing up on my phone

Yes in the home app on her iPad in the Home tab/page , top right are three dots. In Home Settings - Allow Speaker & TV access. I need to change mine to only people sharing this home to keep guests out.

Presumably she has a separate Apple ID then, and has the HomePod set up in her "home". Perhaps it might help if she changed the Allow Speaker & TV Access setting for her home to Only People Sharing this Home.

tt2

I thought I had mine on only people sharing this home today but I forgot I allowed my son to use it a month ago and had changed it to anyone on the same network. The third choice is Everyone, personally there should be Nobody for those of us who live alone and don’t want guests interfering .It really annoyed me today when my grandchildren kept turning off my music with their phones and playing their stuff on my Apple TV! Every time a good song came on that the adults enjoyed, off it went or they skipped to the next track.

Anyways it’s not playing on your phone, it’s just on the Lock Screen to control it.

If the HomePod is sharing a home that you have access to then this behaviour appears to be by design. It allows you to pause or control what is playing, but you don't have to use it.

tt2