I have a 500 (08 reg) and also bought a music adapter for iPods/iPhones etc, but failed miserably to get it to work. All searches say to update the software to 5.5 then 5.6 then plug in the adapter. I tried this several times, very carefully following the instructions, but the update to 5.5 went fine but 5.6 wouldn't work. Thanks to a quick phone call to my local Fiat dealer, I at last have it working! Apparently, just like a computer, if you disconnect the negative terminal of the battery the car reboots and you can try installing again!
I've done this and it works perfectly with my iPhone SE.