I was worried about lines and such traveling from Kansai to Incheon yesterday, but there were no problems. I checked my luggage thinking that screening may be tight, but the girl in front of me at screening sent bottles of green tea through screening, and I brought my Starbucks (they finally have one at KIX) on the plane with me without any problems. I went from the curb to the gate in less than twenty minutes.
So obviously the new rules do not apply to international flights on Asian-flagged airlines. They are, however, putting the no-liquid ban on flights heading to the U.S., so I will have to down that flask of martinis I travel with before I get on the plane.
Update: Going through Incheon for a U.S. bound flight was no big deal and security took no longer than usual.