IJ: i have my accumulators (1-2 and 2-3 i forget the names i believe there b1 and b2 IIRC) mechanically disabled with a steel bar inside the stock spring that only allows maybe a millimeter of movement. When taking off from a stop in the L position there is still a good 2-3 second delay shifting to "2" no matter what the throttle position or road speed when manually shifting.
I believe its a combination of the transmission mechanics and electronics working with each other to make the 1-2 shift. But even with effectively no accumulators the shift isn't much quicker as far as from time of shifter movement to end of shifting process because the initial delay is still there, but the shift itself is a lot firmer and harder.
I know the supra stick eliminates this with the push button shifters because it is done 100% electronically as if the stock trans ECU was commanding the down/up shift. at least thats what I've seen in my research on the product.