Gunpowder was invented in China in Tang dynasty, and it wasn't until a few centuries later that it found its way to Europe. Why was it that East Asian Nations, that is, China, Japan, Korea, and the Jurchen tribes up north, end up having firearms inferior to that of the West?
About gunpowder in Korea:
Korea did not, surprisingly, have firearms until the 14th century. Gunpowder was expensive, being imported from China, and not really used militarily.
The first Korean person who knew how to create gunpowder that we know of was Choe Mu-seon (born 1328, died 1395). Korea was under severe attack from Wokou (pirates) at the time, and Choe thought that gunpowder would help defeat them.
He already knew of the three major components of gunpowder: sulfur, charcoal, and saltpeter. Saltpeter was the major problem, since unlike sulfur and charcoal it was not readily available. Choe, who could speak Chinese (perhaps several varieties of Chinese, perhaps the Jiangnan dialect/language), finally learned the secrets of saltpeter extraction from the Chinese-either from a Chinese merchant named Li Yuan from the Jiangnan region of China who had visited Korea to trade, or by directly visiting China. He had already succeeded in making firearms by late 1377. Firearms were used in a naval battle to beat the Wokou in 1380.
So you shouldn't assume that gunpowder spread quickly throughout East Asia.