At least it's an easy fix. Sounds like it should take care of your problem. Did they show you the crack in the solenoid?
One thing you can double check is the two solenoids that sit on the front of the intake manifold. Those control the vacuum actuators for the variable tumble control and secondary shutter valves inside the intake. It is possible they broke the vacuum line on the solenoid and it would run fine but have a slight vacuum leak on cold start while the tumble control is operated. Just take a look at those solenoids and verify they're ok. It's easy to break those while leaning over the engine replacing the plugs. The solenoid were moved to the back of the cylinder head on 08 and up.
Great post.
To my eye it looks like the shop broke the solenoid and then tried to glue a regular vacuum tip onto it. I would take a close look at yours for signs of glue. You might be able to get your money back for that repair.
+2 wow!! That shop you went to pulled a fast one on you. I would try to get my money back and never step foot in their shop again. Also, leave a bad report on Yelp or whatever other source.