Greetings kat_nyc73,
I would look into the settings of the player that is starting up on its own. If your using a wired or blue tooth headset, some players have an option to start when your headset is plugged in. Also, the player may be responding to a click of your blue tooth set, if your using one.
I would look into the settings and look for headset options. Disable any settings in the player that you do not wish to use.
This info of course is null and void if your using the phone speaker, LOL.
Hope this helps.