Further away Homepod Mini in another room listens/responds to Siri

I know you said they are not configured in a grouping, but have you actually used the Home app on your device to configure them in different rooms?

• Are both devices, configured to use Siri?

Change HomePod settings - Apple Support

• Even though they are not paired, have you tried pressing and holding on the top of the HomePod and say something like "Turn on Siri"?
• Have you reset the HomePod?

Reset HomePod or HomePod mini - Apple Support

That was all I needed to do, including making sure the location in the Home app are in different rooms. I have a stereo pair in my Living Room and a single HomePod in the bedroom and each location works on the closest device. The only problem I have ever encountered is sometimes my iPhone will respond first and I need to turn it upside down, but that is only occasionally. Sorry, I could not be more helpful.

There are 4 mic’s inside each mini listening to you. Try rotating the min left or right in order to get the mic into a different position. This sometimes helps to improve this. Other times it might just go by the last one used.