That last part of “ auto hold” is incorrect, the “auto hold” function uses the ABS system the keep the car put. When you hit the gas pedaal is releases the brake. When you set the gear to “P” (park) with auto hold on, The parking brake Will be activated automaticly,

You manual have to release the parking brake using the parking brake button.

But i did try the “ auto hold” and it looks like the lag is far less then.