Except people aren't so cut-and-dry as to obey simple rules like this. What an older generation was taught was "Chinese" was more along these lines: https://ko.wikipedia.org/wiki/%ED%95%9C%EC%9E%90_%EB%AC%B8%ED%99%94%EA%B6%8C . . .
Of course that doesn't go for all Asians either. Most of Russia is in Asia, say, so they're Asians too, right? Santa Claus was Asian because Saint Nicholas of Myna was from what's now Turkey in Asia Minor, no?