As on the floor the tuck jump on the beam is described as bringing the knees horizontal or higher at peak height.  Taking off and landing is performed with one foot slightly in front of the other.  As the gymnasts get better they can kick out after reaching the peak height of the tuck.  The kick out is done quickly so the athlete has time to bend the knees during the landing.  Observe this gymnast’s quick kick out.

Still 1  – Notice how the knees are up and the torso is leaning forward.