I know that this topic is very old, but maybe my answer will help someone in the future since I spent a lot of time to find the right information.I have had a Littermaid for about 3 years now. You are correct that the box does not turn on & clean out the clumps until long after the cat leaves the box. My 2 cats appeared to be a big freaked out by it the first day or so that we had it, but the calmed down & got used to it pretty quickly. Neither of them has ever been afraid to use it or anything. We have one Litter Maid
https://petapproves.com/best-self-cleaning-litter-box/ & one standard litter box.
Overall I like the Litter Maid because I H-A-T-E cleaning out litter boxes (this, IMO, is the ONLY downside to owning a cat), so it's nice that it scoops out the clumps into the recepticle & closes it off so that I can empty it every few days or so.
The only complaint I have is that my Litter Maid is not exactly maintenance-free. No matter what brand of clumping litter I buy, the rake often seems to get stuck at clumps that are stuck to the bottom of the box. It tries a few times to get through the clump, & eventually it gives up & stops with the rake halfway down the box until I come reset it & manually scoop the clump. It also has a tendancy to scoop the litter up on one end or into a corner occasionally, which also causes the rake to get stuck (even if there are no actual clumps in it, just loose litter piled up too high for the rake to get through).