I have no problems with Entune on my 14 Sienna. I paired my GS4 to the van via Bluetooth. Make sure the van connects to the phone via Bluetooth then run the Entune app on the phone. Hit the app button and it works. Not sure if this is different than the Prius.
Entune works great on my SGS3. In fact, I love it. It's a pretty basic interface but works great for its intended purposes. I don't even have to open the app on my phone, when I use an app in the car that requires internet connection, it just asks me to hit confirm and the app on my phone opens automatically.
This is not normal, and you should take the car to the dealer and have them either show you what you're doing wrong or fix the problem.
You can try updating the Entune software in the Prius to 3.2 What did you do to ur Prius today???? | Page 202 | PriusChat
Entunes continues to work perfectly with my Samsung Galaxy S4 and Android 4.4.2 on Verizon. Thankfully I have the discipline not to look at weather radar or stock prices while I am driving! Better traffic info than I had gotten on my Tom Tom GPS that I used in my previous Corolla.