Wow, thats weird, I haven't driven a late auto 2011 yet... interesting.
So when in Sport mode, you come to a stop, if you then hit the left tap button (to go into manual downshift), it will actually kick the car forward some, as it shifts into 1st gear?
Exactly.. if you have a V8. the V6's are geared a bit different and they will always go to first. You can validate this by upshifting when you are stopped and see what gear it is shows and subtract 1.
The below is taken from a post on another forum, and that's the way it works on mine.
To clarify this a little more:
1. DRIVE: regular driving
2. SPORT MODE 1: Shift down to "M" and push the gas and go! the trans will shift automatically but the shift points are higher
3) is MANUAL mode where the shifter is in M and you use the paddles to shift. You HAVE to up shift but can let the the computer do the down shift. IN this fashion, the computer will put you into 2nd gear and never 1st. To want to get into 1st, you have the tap shift it further.
4) is just like 3) but you control both the up and down shift. This is by far the "sportiest" as you completely control when to shift. There are still protections because the computer can deny your shift, so it's safe.
If you are in MANUAL mode (i.e. tap shifting with paddles) you can remain in this mode as long as you want. Once you put the shifter back to D or hold the right paddle for a few seconds in 6th gear (not in all A6s) then you are out of the MANUAL mode. You will have to move the shifter to M again before you can use the tap shifts.
An important note in M mode, you should think like a stick shift driver to enjoy this mode. Get the engine rev up fairly quickly and and then shift. If you just lightly ease into the gas and shift, the delays (slipping like) will be more noticeable. Test it out and enjoy.
Competition Mode have to do with traction and stability controls and not the transmission.