I took a whole course on this in college (check out the Asian-American studies department at your friendly local university). We discussed what it means to be "Asian" in many sessions. I'd recommend reading some of the work of Ronald Takaki or Gary Okihiro, who are historians on this topic, if you are really interested.
In short, "Asian" means something different in different countries. In the UK an Asian person might be someone of South Asian (India/Pakistani, etc) descent, while in North America, Asian refers to someone of East Asian descent (China, Japan, Korea, etc). However, it means something entirely different to be Asian-American, Asian-Canadian, or Asian-Australian than simply ASIAN.
There's really too much to go into here, and I don't see how this relates to MBTI.