Throttle response is tuned by BMW. Throttle response is the worst in ECO PRO mode to help with gas mileage. Throttle response should be better in Drive and best in Sport mode.
I emailed Burger to confirm that the stage 1 tune addresses throttle response. Because it is drive-by-wire throttle delay can't be completely eliminated.
Mileage is unaffected unless taking advantage of the increased power.