Is the app running? I.e. can you see the Headphone icon in your menu bar (top right corner)? If the app is running and has detected that headphones are plugged in, it should show the Headphone icon with an empty plus sign. If it has additionally also detected that music is playing, the plus sign will be filled.

Maybe try changing volume through the volume keys on your keyboard. That usually triggers the Apple "click sound" to demo the new volume, so then you should see that the Apps icon switches from an empty plus to a filled plus sign.