Customs in Japan from Korea?

I have the below travel itinerary upcoming:
New York (9/28) > Incheon, South Korea (9/29)
Seoul (10/5) > Jeju Island (10/5)
Jeju Island (10/7) Japan (10/7)
Japan (10/13) > Korea (10/13 – layover)
Korea (10/13) > New York (10/13)

Will I be going through customs at the below entry points?
9/29 – South Korea
10/7 – Japan
10/13 – South Korea
10/13 – New York

Additionally, if I buy items in Japan, do I need to declare in South Korea on 10/13? Same instance on 10/7, would I need to declare anything in Japan that were purchased in Korea?

Appreciate any insight!

by krnbttm

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