I have only had my Samsung for a few days, but this has been annoying me too. It seems that the Music app does not close in the usual way by swiping it off the screen or clicking Close All, and so it starts playing automatically next time I open the tablet.
I think I have found the fix, but not 100% certain yet as it is only a few hours since I started experimenting with it. When the Music app opens on screen, it shows 'My Music' in the top left hand corner, followed by a vertical alphabetical listing of Playlists, Tracks, Albums, Artists, Folders or Nearby Devices. If I click on the Options icon in the top right hand corner, there are no settings to stop music playing or close the app.
But if I tap on the square button in the bottom left hand corner of the screen next to the current album/track title, it changes the screen display and shows a horizontal list of tracks on the most recent album played. But it also provides a different set of Options via the icon in the top right hand corner of the screen. One of them is End, and if I select that the app closes and needs to be manually opened next time I use the tablet.
The square button I am referring to is grey on my screen. That may be because of the way I have copied my music over from a pc. I think it should maybe show an image of the album cover, but whether it's grey or an album cover, it's clickable and does lead to those extra options - one of them being End.