My HomePod mini keeps adjusting volume by itself

You can disable “Hey Siri” or simply tell it to “stop listening”. See: Change HomePod settings - Apple Support

If you feel it’s not working at all as it should you can Reset HomePod mini and  set up HomePod again.

Also make sure it’s updated to the latest software

By connected to iPhone are you Playing music on it? If so you might have noticed the Lock Screen on your iPhone displays controls and you might accidentally be tapping on the volume. As to Siri lighting up by itself I wonder if this is a glitch with the current 17.5 version? My gen 2 HomePod started displaying colours the other day and wasn’t the normal Siri colours but the entire top was going crazy with colours. I had to press it to stop. It hasn’t done it since though.

After you restored it on your PC and set it up again you might have re- enabled hey siri. Tell it to stop listening so hey Siri is off and if you need to use hey siri you can always enable it again in settings. This way you can test it for a few days by having hey Sufi set to off to see if it’s an issue with Siri. Siri could be thinking you asked to turn the volume down.

if these issues persist try a reset a different way:

• unplug HomePod for over 24 hrs
• plug back in - wait at least 10 seconds

1. Unplug HomePod or unplug the power adapter for HomePod mini, wait exactly 10 seconds, then plug HomePod back in.
2. Wait exactly 10 seconds, then touch and hold your finger to the top of HomePod.
3. The white spinning light will turn red. Keep your finger down. 
4. Siri will say that your HomePod is about to reset. When you hear three beeps, you can lift your finger.