I'm... not sure that's the actual reasoning of her title, or where you're getting that from. Consider the fact that absolutely nowhere it's said that she judges anything other than Gensokyo souls. And considering that the real Xanadu was the capital of a Chinese dynasty, it doesn't make any sense to say that her jurisdiction involves an actual place called Xanadu; rather, like the wiki states, her title is better translated as "Yama of Paradise" (based on the use of "Xanadu" as "Pleasure Palace" in a poem [which was also refering to the real Xanadu]), which I'm pretty sure is just a rank title and not a literal description of what her jurisdiction is.
Alternatively, it could be exactly that, and "paradise" is just a way to refer to Gensokyo, and maybe other fantastic realms similar to it, if there's any at all.
But all that is pure speculation; going by the only info we have for sure, there's nothing suggesting that she regularly judges souls from outside of Gensokyo (except for every 60 years). Otherwise, Akyuu would at least write "judges all the souls of Gensokyo and more" or something like that on her profile.