In Standing Leg Pump Facing The Chair, it’s the glutes’ job to eccentrically control the pedal. Most students press down using their quad concentrically, but forget to control the pedal on the way up.
Further, if the glute on the side of the body with the foot on the pedal is not working sufficiently, the quadratus lumborum (QL) on that side will take over and you’ll see hip hiking (this side of the pelvis will be higher than the other), and the rib-to-hip distance will be shorter on that side.
To remedy this, press the pedal down and keep it down, using your glute. Then very slowly try to lift the pedal an inch or two, making sure the glute is still active. Only lift the pedal as high as you can keep the same rib to hip distance on both sides.
You'll find a video tutorial and detailed description of this and many more Pilates exercises inside the Pilates Encyclopedia membership.