I was thinking the cuff is inflated completly with the sub surfaced.
Controlled openings of the cuff to deflate would cause the water pressure and air pressure to reduce the cuff air pressure and displacement into the low pressure WTC of the pump compartment. Yes it is very emperical, but it has brutal simplicity.

You do not ever lose your air volume. You are moving air volume and pressure in the vertical tube in the hull. THAT is what causes the sub to change displacement.

I have not tried it yet, but, why would it not change displacement in the vertical tube ?

More thought. Why can't the pump be in the top of the tube and make the operation more failsafe ?

It seems it can work either way. Just preference.