Hi UtahMacTech,
Thanks for contacting Apple Support Communities!
We understand that your HomePod mini starts playing unexpectedly when your other HomePod should be playing, correct?
To start, you may consider restarting both HomePod's and your wireless network. This resource will show you how to restart your HomePod: Change HomePod settings - Apple Support
"Restart HomePod
If HomePod isn’t responding normally, you can restart it. You need to be near HomePod to restart it.
- In the Home app on your iOS or iPadOS device, tap HomePod.
- Scroll down, then tap
. - Do one of the following:
- For a single HomePod: Tap Reset HomePod, then tap Restart HomePod.
- For a stereo pair: Tap Restart HomePod."
If you're still experiencing the same behavior after restarting your devices, you can also reset the HomePods as outline here: Reset HomePod or HomePod mini - Apple Support
We hope this helps.
Cheers!