Her Onmyoudou is a bit different to conventional Onmyoudou... at least, it's different to Type-Moon's Houjutsu.
Basically, the Eastern school of Magecrafts are incompatible with the more 'classical' magecraft schools of the West, as unlike what is taught at the Clock Tower, Onmyoudou in the Type-Moon universe have to 'become one with Gaia', or one with 'spirits'. Basically, it's a bit like sinking with Gaia and its Terminals, compared to Magecraft where there's a bit more of a scientific approach - steps, foundations and self-suggestion. It's using Gaia rather than becoming one with her.
Caster's Houjutsu, as written in her profile though, is just 'Houjutsu' - it's not the said school of magic, but it simply looks like it. In truth, everything that Caster does is to be more proper, related to cursecraft and witchcraft, which are perhaps included in Houjutsu/Onmyoudou's arts, but are only part of the curriculum, not the entirety of it.
This might actually sync in with Uchiten even better because she feels more like a demon (which are materialized curses in Fateverse) than a Fox Spirit (an aspect of a Divine Spirit, aka Amaterasu). Her shikigami are also comparable to being materialized curses rather than familiars animated by magecraft.
