Do you use sensorly? If so I think i will uninstall and see if that resolves it. The only other modification I made to the device was rooting to install gmail 4.2, but I unrooted and flashed back to stock so I could receive the jelly bean firmware update. Of course that being said I also used the zip file to update to JB that was provided here because the ota firmware update was taking too long.
So it can only be three possibilities in my case.
1. Root broke some piece of firmware.
2. Sensorly or another background service is initiating the startup
3. The zip I flashed had some error in it
Although based on what I have heard from a few people with similar issues, there may be an issue with the JB update caused by the dual voice action services (Google now and svoice conflict) where the phone is accidentally "listening" and believes I wish to start the music player.
Either way there is something going on. On a completely (un)related? and humorous note, I have experienced the music player starting inappropriately long before any mods, rooting or the latest firmware update. I used to mess with svoice and ask it inappropriate questions. When I would address svoice as a person and say something obscene directed at svoice, it would open the music player and play a song. I thought Samsung may have just had a sick sense of humor and flagged certain voice prompts to do something completely different from the intended result.
Who knows, maybe svoice is somewhat self aware, she did tell me on several occasions "that is not a very nice thing to say" or similar response when I used profanity. Go figure.