I just started an Apple Music trial last night. You need to turn on "Sync Library" in the iphone Settings menu. Once that's turned on, the playlists from your phone app should all sync onto the car's app. It seem to take a while initially when I was looking to get a test playlist to sync up, but after a while all the playlists I ported from Tidal was sync'd relatively quickly.
BTW, if anyone from Tesla or Tidal is reading this, I'm most likely switching to Apple Music solely because there is no effing shuffle button for Tidal in the car.