You have a JBL amp that powers everything (located behind the plastic molding in the passenger rear cargo area to the left of the sub). The stock head unit just provides a signal via a digital link (as I recall reading). I am not aware of any modules to allow the adding of an aftermarket head unit.
The rear pillars and center channel are on the same circuit off of the amp. The amp is most likely not sure what it is receiving and how to process it. Especially since there is only 1 2 DIN head unit on the market for 5.1 surround (kenwood execelon at $1900 unless on sale).
Nothing is simple with this JBL system. If you change out the front speakers with components, you are fine. But not in the rear doors. They are 2 ohm speakers. Adding standard (4 ohm) speakers cut the volume in half. I found out the hard way. I put components in with the tweeters in the rear pillars. I had to adjust the front/rear fade to make it listenable (is that a word?? LOL)
The shop you got the work done should have been aware of these limitations. Unless you plan on investing in amps and new speakers all around, you may need to take it back, get a refund and have the old unit installed. Square pegs just don't fit into round holes.
Hope that helps.