Just got a second echo installed, and configured it in a multi-room setup. The new unit is upstairs and today I triggered the “Start my day” routine. Unfortunately when it responded it didn’t deliver the information back to me on the echo that received the command, but downstairs in my original echo - which as you can imagine is not particularly useful. Also based on the FAQs it was my understanding they are supposed to be proximity based so I would have expected it to play back the response in that up stairs unit.
Also just to confirm, I only added both units to the Everywhere group for situations when I want to pay music across both devices.
First try resetting the device. Your placing the device into a Multi Room Music Group should have no effect on whether it hears your commands or not. The behavior you are describing is very weird. As I always do I suggest you contact Amazon directly. In the Alexa app go to Help & Feedback and choose a method to contact them.