Do not disturb fail

When I set my phone to do not disturb and then use my AirPods to listen to meditation apps or music, calls will start ringing in my ear interrupting my meditation or my music, and Siri keeps trying to notify me of incoming texts. Does do not disturb cease to function once I put my AirPods in? Do I need to use a different setting to avoid interruptions in these cases? It can be very annoying.