HomePod Mini music issues

I purchased HomePod Minis for my two daughters to listen to music in their rooms. They both have Apple IDs that are part of our family setup. We subscribe to Apple Music through my Apple ID, and the subscription is shared with my family. The kids both have iPod touches with their own music libraries, playlists, etc.

I have two problems:

1. When my kids ask their HomePod to play a song and it begins playing, I look at my phone and the song is playing off my Apple Music. I then cannot use my phone to listen to music without stopping their music. Why is it playing off my library? I specifically set up the HomePods with THEIR Apple IDs and THEM selected as the primary users. I want them to be able to play music without me being involved. And I don't want the music they play influencing my Apple Music suggestions, play count, etc. How can I get it to "connect" their Apple Music and not mine?
2. The HomePod cannot seem to recognize their playlists or songs. My daughter will ask to play one of the playlists she's created, and it will say "I couldn't find that on Apple Music." But the playlist is in her library. What is the deal? Something tells me there's going to be some Apple Match or iCloud syncing issue that I'm going to hate. I don't want songs and playlists synced across all our family devices. I want each person to have their own Apple Music library with their own curated songs and playlists.

Any ideas on these issues?