I've experienced the same thing, but I can add a couple more specifics. Bear with me as I have an iPhone for work and an Android for my personal phone.
Occasionally I have the iPhone on BT actively playing music and park the car and switch off the ignition. If I leave the BT set "on" on the iPhone, when I return to the 4R and fire up the ignition, the reconnect to the iPhone via bluetooth sounds very "choppy" and I have to toggle the BT setting on the iPhone off and then on again to get a clean connection. I never have this issue with the Android, i.e. I can leave the BT setting on the phone toggled on, switch the car off, and when I come back and fire the 4R up, it'll just reconnect cleanly and restart whatever music I was listening to when I parked.
If I attempt to connect the Android phone after having had the iPhone connected via BT, once the connection is made the 4R seems to want to grab any music on the Android it can sense (as you described), usually whatever I have loaded on the Play Music app (Android / Google music app). That is the only time that the Entune / BT seems to grab whatever music it wants as you're describing.
I don't know whether you're having this issue when switching between phones, but shutting the BT functionality on the phone itself off either before or after shutting the ignition off seems to alleviate all the issues even though this extra step theoretically shouldn't need to happen.