I would start with the Moto app, Meeting Mode. Open Moto > Menu (gear symbol on top right) > Assist > Meeting > If Keep Quiet is checked then the phone will go into "Priority only notifications" when a calendar appointment is set as "Busy". See if that option is checked. If you don't want priority mode, un check Keep Quiet.
Edit: Check the Sleeping option also, underneath Meeting. Sleeping mode will also set notifications to "Priority only" if it is turned on, and set up for the time you normally sleep.