Confused by Korean names

I'm watching the credits of a Korean series, and some actors seem to have their names listed the way they are pronounced in Korean, like Kim Mu-yeol (김무열), for example. Others (usually the lesser-known ones) seem to flip their names to the first-name/last-name format, like Sung-Jae Kim (김성재).

I tried checking the guidelines, but one section says names should be first name/last name, while another gives an example that seems to favor keeping the order used in Korean.

My question also extends to Japanese names. Most entries on IMDb seem to reverse the order, placing the surname last, should it really be done that way? Or should we keep the order used in the original language (surname first)?