The account is that after the war, Korean residents living on Tsushima were eating this, and it spread across the island from there. Local butchers then adjusted the seasoning toward what Japanese customers wanted.
Pork is steeped in a marinade built from miso, soy sauce, garlic, and chili until it has taken the flavor all the way through. Then it goes on the heat. The exact blend differs from shop to shop, and some of them grate apple or onion into it.
Tsushima sits in the strait between the Korean peninsula and Kyushu. Look at a map and Busan is closer than Fukuoka is. Given that, the fact that the island's grilled meat descends from a way of cooking from the other side of the water is not a curiosity or a coincidence. It is simply what geography produces when it is left alone for long enough.
You can eat it now at set-meal places and izakaya, and frozen packs of it sit in the island's supermarkets and souvenir shops, which is usually the sign that something has stopped being a specialty and become ordinary. It gets cooked in houses as much as in restaurants. An island in a strait takes things from both sides, and after a few generations nobody is keeping track of which side each thing arrived from.
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