I think this is a cause for confusion from most people about the Do-Not-Disturb (Bedtime) Mode on these watches.
You can have 2 settings for this:
1. Have it put the WATCH ONLY in DND
2. Have it sync DND with your phone
When you have it synced with your phone, it will follow your phone's policy on which calls, messages, notifications to allow.
When it is NOT synced with DND on your phone, you put the watch in Bedtime Mode and it silences all notifications on your WATCH ONLY.
At this time, there is no way (at least where I have found) to set the watches DND to allow things to pass through on it's own when not synced with DND on your phone.
Hope this helps and clears things up.