The update is apparently rolling and you should see a notification on your phone soon or you can check manually if the update is available to download.
Meanwhile, the Galaxy S III in Korea is getting the Android 4.1.2 update too and will be available over the air or through Kies.
Updates had been due to take Samsung's Premium Suite features, which includes stuff like multi-view mode, new Gallery app, Paper Artist app, improved notification panel and much more.