Even if you are vaccinated outside of Korea and vaccinated with one of the vaccines that Korea approves, that does not give you automatic quarantine exemption in Korea. As of August 2021, you still have to apply for Quarantine Exemption. Does not matter if you are Korean or a Foreigner. If vaccinated outside of Korea, you will need a Quarantine Exemption certificate before you arrive in Korea.
There was a short time period where Korea did not recognize people vaccinated outside of Korea. I believe starting July 1st, Korea recognized certain vaccines from certain countries, and then you have to apply for Quarantine Exemption.