I can see why the car feels like it has turbo lag. The MK7.5 is a very different-feeling car from my DSG MKV (mine had the FSI motor, they switched over to the TSI sometime during the 2008 model year) and manual MK6. Handling is noticeably better, especially with the LSD up front, but the throttle tuning (as many here have pointed to) really isn't doing it any favors.
It doesn't help that the DSG is set to shift so quickly to higher gears either. I don't think the revs go over 2.5k in regular driving. I feel like I have to press the gas pedal down a lot to get it to stay in any gear longer. Using "S" or the paddles helps though. That aside, downshifts are disappointingly slow when trying to force them by pressing on the gas pedal. Using the paddles to quickly drop 2-3 gears is pretty easy too.
All that aside, it's stuff that's relatively easy to adjust your driving style to or work around, but I do wish the DSG was programmed to be a bit more responsive from the factory though. I had a Madza CX-9 that downshifted more readily than the DSG does, but that's not to say its transmission wasn't without its own faults either of course.
All these reasons are why I went with a bms pedal tuner even though I'm dsg tuned already. The dsg tune helped a bit but the pedal tuner made it how it should've been from the factory. Direct input with zero throttle lag vs. having to keep pushing the pedal down hoping for a downshift but usually boosting it hard in the gear you are in. I don't think it has as much impact on a manual car as a dsg. Also installs in 5 minutes so warranty friendly if you need to take it out.