Are you verbally setting the alarm? As a "better than unplugging it" bandaid, try turning off the microphone using the switch on the base.(if yours has one) There seems to be a recent common issue where multiple speakers are now responding to a spoken command. It used to be that even if multiple devices heard you, they would negotiate to figure out who was the closest so that only that one would respond. It seems that functionality may have been broken , perhaps as an unintended result of the changes they made after losing the sonos lawsuit. I have seen some people mention that doing a factory reset on the speaker(s) seems to fix the problem but I haven't tried this yet.
Another option could be to go into the settings for the baby mini and set the alarm volume to zero. Under settings, select Audio, then select Alarms & Timers, then you will see a volume slider, which can be set to zero.
