Cats (and kittens) do ometimes seem to be able to "hold on" if they are nervous of their surroundings. If you are keeping him in the dog crate for his/her safety, make sure that s/he cannot get head stuck in the mesh

Their heads are a lot smaller than puppies!!! Also, put the litter tray in the crate, posibly with a box acting as a "hood". Are you using the same litter as the breeder? I always make sure that kittens leave home with a little pack of "used" litter as well as a pack of the litter they are used to & advise the new owners to sprinkle the "home" litter on top of the new tray, just to show kitten where to go.
Do make sure that you leave water down.
Margot