In my experience, you go through immigration in the first airport at your destination country or customs region (the Schengen area, for example), whether it's your final destination or not.
When returning from Asia, I always go via a West Coast city (lower costs even with the added domestic flight, more choice of airlines), and that is where I go through immigration, even though my final destination is Minneapolis.
So while I have not flown domestically in Korea, my experiences elsewhere tell me that you would go through immigration in Incheon and only ordinary check-in and security for your domestic flight to Busan.