Asian Names

I was wondering which is the more acceptable order for Asian names (in this case Korean/Chinese): family name first or family name last, as in the Western style? In this instance, I'm referring to something being written in U.S. English.

I was writing a review of the movie Mother (Madeo) and Bong Joon-ho (as well as well known filmmaker Wong Kar Wai, for that matter) seemed to suggest the former, despite that their imdb entries list their family names last (Joon-ho Bong and Kar Wai Wong).

This extends to Japanese names, too, amirite? Why do Westerners have to confuse one another and have Wikipedia entries for Michio Miyagi, instead of vice versa?