Hi, I'm starting this post in the hope that someone googling for this issue will find this solution useful.
Admins - feel free to re-categorize this post and/or mark as Solved. If more info is needed, just let me know.
Home setup - I have multiple Google Home speakers in my house. All speakers have been appropriately named and assigned to the Home group, as well as proper Room groups. All speakers are functional (i.e. Online, visible from the Home app, will play media, etc etc). One speaker (the Living Room speaker) is a Nest Mini. The rest are Google Home minis.
Issue - When I would set a timer from my Kitchen speaker, the response would come not from the Kitchen speaker as expected, but instead from the Living Room speaker (the Nest mini). I noticed the Living Room speaker would respond to other commands given to other speakers as well, but I can't say for certain what or how often, because I generally only use the timer function in the Kitchen anyway, and cast Spotify directly to the device I wish to use at the moment (this functionality works fine). In short, it seemed that "Ok Google..." command responses were being routed to only one speaker (Living Room speaker), instead of coming from the originating speaker.
What Did Not Work for Me - Rebooting the devices did not work. Completely deleting, re-adding, and re-configuring the Home and it's Devices did not work. Adjusting the "Hey Google" sensitivity (Home App > pick device > Gear icon > Device Features - Audio > Google Assistant - "Hey Google" Sensitivity) did not work.
What Fixed the Issue - While scouring through all the Devices and their settings, I noticed this setting:
"Let others control your cast media"
It can be found in the Home app by going to the device, then the settings Gear icon, then Recognition & sharing.
In my Home setup, this setting was turned ON on the Nest Mini (Living Room speaker experiencing the issue), while also being turned OFF on every other speaker device in my Home. I don't recall ever turning this on when I set up the device, but who knows, maybe I did on accident or it defaults to having this setting on. Regardless, I switched this setting OFF so as to match how I had the other devices set. After changing the setting, I rebooted every speaker device for good measure. Then I tested by trying to set a timer from the Kitchen speaker and... Viola! The speaker responds as expected! No more responses from the Living Room.
I'm not sure exactly how or why this worked, but it did. Hopefully this solution helps others who are getting "Ok Google" command responses from the wrong speaker.
Below are links to some posts that DID NOT fix my issue, but nonetheless may be related. If you stumble on my post and you've already tried the solutions below and they did not help you, my solution may be what you're looking for.
https://www.googlenestcommunity.com/t5/Speakers-and-Displays/Google-Nest-mini-timers-on-multiple-dev...
https://www.reddit.com/r/googlehome/comments/bm4lh0/the_wrong_google_home_responding/
https://support.google.com/assistant/thread/############/google-assistant-responding-on-wrong-device...
https://www.googlenestcommunity.com/t5/Speakers-and-Displays/The-wrong-device-a-speaker-in-a-differe...
https://www.googlenestcommunity.com/t5/Speakers-and-Displays/Multiple-devices-responding-at-the-same...
https://www.gearbrain.com/google-assistant-checks-response-mistake-############4.html
