After a couple minutes of being in your car, look at the notification bar on the top of your phone and see if you see the play sign (sideways triangle) that indicates your music player is going.
I have a Ford with Sync as well and whenever the bluetooth connects, the phone assumes it's a bluetooth stereo headset and that you want to listen to your music so it starts the player. When you get out of the car, the bluetooth disconnects and since the music player is still going, you hear it out of your phone's speaker.