I use Map my Run.. The one time that I used Apple Music I had issues with the app not tracking my run.. Luckily I caught it early, and closed Apple music and map my run.. Reopened Map my run, and switched back to Spotify and the problem went away.. Not sure which app it was, but i've not had an issue since, but I've not used Apple music since either..
I ran a 10K last weekend, and couldn't for the life of me get my watch to start map my run (first time this has ever happened).. Before I noticed it I was about a half mile in and already getting a little sweaty.. Pulled my phone off my arm and started it through the app.. Once Map my run was open and started on my phone my watch picked it up without any more problems.. I've ran twice since and not had any issues.. I chalk it up to being nervous for my first race, and I just missed it at the start...