Bleeding hydraulic systems (of air) is a common requirement, although some have self-bleeding capabilities built-in if working correctly.
Hydraulic fluid is essentially incompressible but a tiny amount of air can compress easily making a hydraulic cylinder act mushy, like an air spring.
I would hope the owner's manual addresses bleeding requirements if they are needed. In any case, I would look at the stabilizers (without getting under RV) while someone is moving around the RV to see if I can see any movement of the cylinder rod going in and out. It shouldn't move at all if working right.
It's hard for me to imagine that a hydraulic cylinder bolted directly to an RV chassis wouldn't be much stiffer than the RV's suspension and tire's if it's installed and working right.
I also have noticed the rocking when my leveling jacks are down, however, I did notice that when the levelers don't have to lift much, its alot stiffer than when the tires are lifted off the ground, so I try to position my coach to make it as level as possible before deploying the jacks. Sometimes, I win, sometimes I lose!
Leveling with jacks alone touching ground results in movement via the metal shafts flexing. Cut a bunch of 2x12 pieces to 12" long and put as many as possible under each jack foot/pad before leveling. Once level there is only a couple inches of shaft being used so less flexing. Whenever possible keep all tires on the ground for additional support. It will still move some - but not as much.