It was mentioned in this episode that Jon has French, Welsch, and Korean roots. His father was a Caucasian man with French and Welsch in him, while his mother was Korean. Jon's family has such strong Hawaiian ties because his mother was born and raised there.
All of the Gosselin children are mostly Asian-looking, since that gene is famously dominant, but in this episode, the kids decided that sextuplet Alexis looked the least Asian.
Mady: Guess what? I'm the Asian-est person in the whole family, besides Daddy.
Jon: We have some kids that think they're more Korean than others. We have some kids that think that they're the only Koreans in the house, and that all the other kids are just white.
Kate: And then they'll get mad and go, "I'm Asian too!" And they have arguments at the table, in the car, of who is Asian and who is not, and then it always boils down to the fact that me and Alexis are the only two non-Asians, which is not true, even so.
Kate: (about Alexis) She even considers her stuffed animal Dusty to be Asian.
Jon: "Is Mickey Mouse Agian?"
Kate: Yeah, that's what she asked us last night.
Jon: And I said, "No, Mickey Mouse is just a mouse, honey." [Alexis said], "An Agian mouse?" [I said] "No, just a plain old mouse."
Kate: A plain old mouse. (laughs)
Jon: With red underpants.