That didn't work for me either, but I figured it out. Here's what you do....
Download Spotify from the psn store
Save a bunch of songs, albums, playlists etc (I highly recommend the Slayer playlist \m/)
Quit Spotify and load the game
When you get to the garage, go to the menu to turn the music all the way down
Hold the ps button down to bring up the menu
Go down to music, then right on the control pad
It will say something like "You must allow the psn to see your playlist to something something"
Go down til it says sign in to psn or whatever it says and sign in. Idk if that's necessary, but that's what I did
Then go right on your music and pick where you want it to start playing
The music will start, so hit the ps button to return to the game, with your music playing
Drive and jam!
You'll have to listen to a commercial once in a while, and the engine drowns out the music a bit, but it works. I haven't found a music volume menu.
