Congrats on the new purchase! I love the Cali's and you picked one of the best colors IMO (Black and GB) but im biased. I would say the lag you are experiencing is a combo of both undergearing and the automatic. My wife has the auto (v6 granted) but the auto is stock tune is far too smooth. It is much faster than it feels though, it's deceptively smooth. Throw some gears in and a tune if youre not concerned with warranty and she will be singing a different tune. Also don't forget to check out gtcsregistry.com, and you can order your limited production certificate from fordshowparts.com.
HIS: "Night-Mare": 2012 Mustang GT/CS, Black on Black, MT, 3.73 Gears, HID's, Security/Comfort/Electronics Packages. #2 of ????
HERS: "Blue Steel": 2012 Mustang V6, Kona Blue, AT.