Rough Cold Starts / Idle After Intake Manifold Replaced

I just had the intake manifold replaced under the extended warranty as well as the purge valve on my wife's 2012 GTI. Car ran with no problems prior to these replacements. Dealer indicated that I should also have the carbon cleaned for $315. Strapped for cash, I declined. I also had the intake manifold changed twice on my 2010 GTI with no problems which is why I passed on the cleaning.

Immediately after the service, the car experiences rough cold starts and idles between 2-3K. The dealer explained that the carbon build up coupled with a new intake is causing the rough cold starts.

Doesn't make 100 percent sense to me. Could it be something else besides the carbon build up?

Make sure the vacuum lines are all attached which control the solenoid to the flappers. Also manually move the flapper arm on the right side of the manifold.

There is an air leak post throttle that needs to be addressed.