I don't think this will be particularly different from the usual case of an empty elevator in free fall. When the elevator hits the bottom of the shaft, the elevator and everything inside must come to a stop over the course of a fraction of a second. Whether or not the elevator is filled with water, the person inside will experience sudden and dramatic acceleration when it hits the floor (i.e. they will go splat). From even a drop of just 20m, the person is traveling at 72kph when they hit the floor, and 0kph very shortly thereafter. That's going to hurt no matter what, regardless of if the person is stopped by the elevator floor or a layer of water.
Even if there are buoyant forces due to pressure gradients when the box of water hits the floor, anything that moves the person toward the ceiling of the elevator will only increase the acceleration they're experiencing, making the collision even more deadly. You might get some interesting physiological effects from the pressure shockwave traveling upward through the water, but there's nothing here that makes the situation any more survivable than your typical falling elevator.
To use this superpower to survive, the hero needs to fill the elevator shaft at the very beginning of the fall, and empty it slowly to gently bring the floating elevator to the bottom. Stopping suddenly at the bottom is going to be bad news no matter what.