"Our phylogeny indicates that the two human-associated mite lineages do not share a recent common ancestor and likely have separate evolutionary histories of transmission to humans."

Since it is common for many species of mite to live on a host. It is logical to assume the ancestor for dog/human had multiple species of mite. These would already be genetically distinct and remain so through lineal transmission and speciation of the host. In this likely scenario, the progeny of each distinct species (now in different host species, and different species now having experienced a long period of reproductive isolation) would be EXPECTED to still be more related to each other than the other mite species on the same host species.

Or maybe they jumped species from dog <=> human. It's the more interesting hypothesis, but there is no evidence to say it was more likely than the vertical transmission story which is expected to happen at least sometimes (if not most of the time) in symbiotic sister species that tend to stick to their host species specifically.

Host species switches may happen, and especially in cases where animals are in close contact, which humans and dogs have had. But it sounds like we're still not sure if these mites can even be spread through casual human to human contact.