Does Spotify give you an error when you open it from Android Auto? If you get the error you see in the image every time you want to listen to Spotify, you can try a small change in the permission settings to solve it.
Just go to Settings >> Applications >> Manage Applications >> Spotify. And under the "Permissions" section, activate the "Automatic start" option. Restart the mobile to ensure that the change is applied and voila, it should work without problems.