Asking 3 more times about ingredients finally yielded this answer:
We regret to inform you that we do not have that information. Missha US is an online shop where we sell the products in the US. The Headquarter/Manufacture, will know the answer to that question. Please email firstname.lastname@example.org for more details. Thank you.
And there you have it. Missha is NOT cruelty free, and they possibly test ingredients on animals making them ineligible for KARA's list.