I want to say that in one of the commentaries, Whedon said that, in all honesty, no Asian actors ever auditioned for them, but I'm not sure if I'm just imagining that or not.
That explanation just wouldn't fit with his portrayal of a future heavily influenced by Asian culture. If that's the future he wanted to portray, he could've ASKED agencies to send over Asian actors to audition for him.
...Unless the lack of Asian people was eventually going to be explained. Maybe there was a genocide before the exodus from Earth.