I also hope to keep some Cyphomyrmex wheeleri, and I have found a new nests around my area. The Cyphomyrmex in that area mostly carry chopped down vegetation. There are not many caterpillars nearby the area, so I would think that these Cyphomyrmex are not too reliant of caterpillar frass. The few caterpillars present are never near the Cyphomyrmex nests. Although that's just speculation. I have also been told that C.wheeleri do not use a lot of frass, but I do not have a proper source to reference as proof. However, there are lots of small dark beetles around the same areas. Crickets are also present in a portion of the areas, cockroaches as well but in smaller numbers. So if these ants do take frass, then it is probably from one of these other insects living nearby.
The Antwiki does mention this, "Skeletal parts of dead insects, principally fragments of coleopterous elytra, have been found inside the garden; they were probably added to the structure in order to give it consistency. The ants attach the refuse as a flat mass to the undersurface of the stone, or more rarely dump it outside the entrance." I have not digged up any of the nests to see the fungus myself.
These observations are not definite proof of their diet, but I wanted to throw out some details I have observed. Good luck with your Cyphomyrmex keeping and welcome to California.