Well, it seems that at some point Caliborn learns how to imbue himself and his followers with cherub reproduction power, which is usually only accessible while they are mating. This power is shown through flashy colored lights, and we see it in the Handmaid, Lord English, and the Condesce. Its primary power is immortality (although another mating cherub can still do damage) but it seems it also has other magical powers. In the Handmaid’s battle with Scratch, we see her use some sort of ‘clockwork majyks’ spell, not that it does much good.
It’s probably some sort of physical manifestation of Time crossed with cherub powers and possibly boosted with the power of the juju, but I don’t honestly know how Caliborn taps into it. I think the God Tier clock may play a part, but exactly what he does… still a mystery. Probably a very plot important mystery, too, because if we know the answer then there may be a way to break it.