Pressing the Action button when the prompt is not displayed jettisons the parachute.
After deploying the Parachute, a prompt appears to start the Diversion by pressing the Action button.
This Diversion can only be started while a Parachute is deployed. Landing in centre of the bullseye earns 3 Gold Stars and unlock the 'no falling damage' reward. In Saints Row 2, the goal of Base Jumping is to land within a bullseye while parachuting. Note the target on the lower left mini-map on the HUD.