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.