The chlorine is introduced from the bottom up in The Liquidator -- when you add more chlorine you do so via a tube entry point that is near the bottom of the container. The pool water is introduced on the top. The two layers do not mix if carefully and slowly added -- turbulence in the container is kept to a minimum -- so the chlorine on the bottom remains at high concentration, but only because there is continual water flow in the top layer.
If you were to leave a container of chlorine (bleach or chlorinating liquid) still for a long time, then a small gradient of chlorine with slightly higher concentration on the bottom and slightly lower on the top would result from gravity, but normal diffusion (Brownian motion) will keep things relatively well mixed up so this difference is not noticeable across the relatively small size of the container. This isn't like oil and water where the two substances aren't attracted to each other -- water and chlorine ARE dissolved in one another and that is the lowest energy state. The reason that the Liquidator works as it does is that you do not let things sit and diffuse. If you stopped the flow into and out of The Liquidator, the chlorine on the bottom would eventually diffuse into the pool water on top until you had a container full of diluted chlorine (in fact, you can do such an experiment with bleach or chlorinating liquid in a clear container and then very slowly adding water along the side from the top and then seeing how long these two layers take to mix). Instead, The Liquidator is constantly having pool water flow into the top layer on one side and out of the top layer at the other side. This continually dilutes any "excess" chlorine in the water layer.
So essentially, there is continual diffusion of chlorine from the lower layer to the upper layer, but the continual flow of water in the upper layer keeps the upper layer relatively low in chlorine concentration. The higher density of the chlorine layer tends to keep it below the water layer which is of lower density, but at the interface there is diffusion of chlorine (and some salt) into the water layer and water into the chlorine layer so the interface between the two drops (gets lower) over time. If there was not constant water flow in the upper layer, the upper layer would get more and more concentrated in chlorine until the interface went to the bottom of the container and the last of the chlorine diffused.
What is interesting is that the rate of chlorine introduction should mostly be dependent on the rate of chlorine going from the chlorine layer to the water layer so the fact that changing the flow rate makes a difference probably means that the flow rate affects the average chlorine concentration in the upper layer. If the flow rate is slowed down, then that concentration becomes higher and that will slow down the diffusion a little at the boundary. If the flow rate is faster, then that concentration becomes lower and that will speed up the diffusion a little at the boundary. It might be interesting to sample and test the chlorine level of the water in the upper layer -- it should be higher than that of the pool water but lower than that of the chlorine layer, but I don't know by how much.
Another interesting thing that happens in The Liquidator is that the chlorine apparently diffuses across the boundary faster than the salt so the lower layer becomes saltier over time, even precipitating salt (according to their documentation). I'm not sure why that occurs, but perhaps the salt has a greater affinity for being near chlorine than it does being near water. The salt water is denser than non-salt water, but that still wouldn't explain how the lower layer can get so concentrated as to precipitate salt unless there was some sort of affinity (lower energy state) difference.
Richard