I've used all sorts of shampoo in the Sullivans fogger. You need to put the right insert in the nozzle. It comes with 3 and they are different colors. One of them works good with all types. Can't remember which color it is though. Trial and Error.
A guy I help out some with his sale calves uses all different types of shampoos in the foamers, even cheap human stuff at times. You can tell the difference in the quality of shampoos but they do all work fine.