I played music for 20 minutes to test. I did't completely exit Music, I just switched back to the home screen, scrolled around home screens, opened and closed a couple of apps, went back to music, opened and closed mini-player a couple of times, changed between albums, artists, and songs, and called it quits with no strangeness.
Okay, well be sure to come back here and let us know when yours starts to do it too. I find it hard to believe that your iPhone 6 doesn't have any issues when I tried it on a completely fresh install with nothing else installed, and all setting set to default.