In Europe we applied summer time this Sunday. I noticed that while my phone switched to new time, my Vivomove style showed the old one until the next (manual) sync.
1. This resulted my alarms being out of sync.
2. This could have been critical if I'm based on the wakeup call from my watch for reaching any services on time.
As a comment: yes, my connect app was running in the background (I explicitly allowed it in my android device).