I called a vw dealership (in South Australia) today because I have an iphone5 and a Tiguan and experienced the same thing (after i had purchased the lightening/30pin adapter).
I was advised that the media interface software is not compatible with iphone5. VW will eventually update the software according to ol'mate at the dealership, but it will be at an expense to the consumer allegedly.
I know that there is a iphone/vw media cable one can purchase from VW however, I believe this to only work with iphone4 or older?
Maybe try an older generation ipod to use for the car if all ur music is in itunes?
if anyone can correct me, I'd be more than happy to know... going to try my older generation ipad and see if there is any truth to the tale.... eventually. Until then i'll stream via bluetooth :-)