This is probably a problem caused by Android and the apps installed on your phone. To me it seems that certain apps claim "priority" over others as audio players, and force themselves to open when Play is pressed on the watch. And it's not only the watch, with certain apps I get exactly the same problem with regular bluetooth headphones connected to the phone. So there's probably very little Garmin can do.
But of course you can always start your app using your phone, and then continue controlling it using the watch (at least that works for me).
