The exact origin of the word Nani Kore is hard to define as their is no detailed information on the internet.
Some of the furst instances of the term being used date back to the early 21st century, around 2002-2003.
With the growing popularity of the japanese culture the term has been more and more present in modern day eastern comics.
The spread of Nani Kore before the internet is impossible to define as there is no detailed information.
After the internet was fully developed and the hype around Manga/Anime and everything japanese came into full fruition, the term has spread quickly on a global scale.