I suspect it is still downloading music from the setup. If it does download over cellular. The way Apple does it is it first just setups the placeholders for the apps and content so the phone can start working, but then continues to download the actual apps and content in the background, sometimes for many hours depending on how much you have. So even if it said restore complete, it was not all the items but just placeholders. At least that is the way it works on iCloud.

If it is setup downloading of purchased music, turning of music app data may not stop it since it is setup and not buying new music. Also, I have seen in the past where after turning off cellular data for an app, you need to reboot the phone for it to effect.