I can finally get Pandora to play in my PriusV. But when I turn the car off it starts to play on my phone and I don't know how to stop it. Sound familiar, anybody?
It sounds like you are using the Pandora app on your phone rather than the car's app. If you are using the phone's app, it is normal for it to continue after you shut off the car.
It's the predicted behavior: turning off the car ends the bluetooth connection to your phone; it's the same as if you disconnected your earbuds while listening to pandora. Now would be a good time to become familiar with Tasker (Tasker - Android Apps on Google Play) for Android. In short, you can set your phone so that once the Bluetooth connection is lost (ie when your car is shut off), the media volume immediately goes to zero. And you can define that when it connects the next time the media volume turns back up to "10" or "11" or whatever level you prefer. PM me if you want to try this out. I'd be happy to help. I also own a Thunderbolt.