I highly think the instant torque is the main factor. I don't think people quite understand how much faster the torque comes on when you press the pedal.
I was experiencing this also. And was able to recreate it. If you delay your accelerator a half second in this maneuver the car feels VERY solid and planted. I think being used to an ICE and having a slight delay between throttle and torque to the road, when doing a timed maneuver like a lane change, you compensate for the lag. And in turn press the accelerator early. What happens is instead of having the torque really turn on right as the cars weight is settling, you are hitting the accelerator, as the weight is shifting. I think TC might kick on for a brief moment, but the main cause in applying a lot of torque as the car is shifting weight.
Also note that the Model S picks up crosswinds very easily, and this can have a similar, but not exactly the same, feel. I have adapted my aggressive lane change maneuver accelerator timing and am not having the same feeling you had, and I previously had.
Spend some time changing lanes and trying to feel the car's weight shift. The low CG and limited body roll make this harder than a regular car. Then think about when you really want to start accelerating. My guess is you are pressing the pedal about 0.5s too soon.
