Under Chinese influence basically.

Korean and the other languages in the Sinosphere have borrowed a lot of vocabulary from the various Chinese languages, and the introduction of Chinese writing certainly helped increase the number of borrowed vocabulary and calques. They might have found Chinese numerals to be useful when communicating with the Chinese and other Sinosphere States, or they simply found the numerals easier to say.

Whatever the case, lots of languages in heavy contact with a prestige language does this. Filipino for example has borrowed Spanish numerals for telling the time, the dates, your age and when counting bills. Nowadays, English influence has resulted in the introduction of another set of numerals which has been slowly replacing the Spanish and even the native set.

Another example would be the Romani languages borrowing Greek numerals, but the Greek numerals they borrowed completely replaced the Indo-Aryan words they once supplemented.

Another example of two sets of numerals would be among the sheep herders of Northern Britain. The numerals they use to count sheep is descended from the Brythonic languages in their areas, even if they have been English-speaking for more than a thousand years. They were simply accustomed to that way of counting, and they retained the numerals even after so many years.

In conclusion, it all boils down to contact with a prestige language. Korean speakers borrowed the Chinese set of numerals for a multitude of reasons, however the new set did not completely replace the Korean numerals, probably due to people already having been accustomed to using them.