As far as I can tell you've misread the article. The grandmother of one of the emperors may have been Korean but the first (non-legendary) emperor was Jimmu who was born in Japan. I'm also a little wary of that article since it says "Yamato is the name of the family that founded Japan's imperial line" when Yamato is the word used for the ethnic group to which most Japanese belong. I'm wondering if there's a link here to the idea that Yamato people are mostly descended from the ancient Yayoi who took Japan from the Jomon and were probably from Korea (but not the ancestors of the modern Korean people).

Yamato is also the family name of the Japanese Imperial family.

These facts are directly related, through the Yamato region, from which the Yamato family ruled for some centuries.

Thanks