There were actually three outbreaks of the Plague, but I am assuming you are referring to the Black Death (which happened in the 14th century), so I will answer it. The Plague was caused by the bacterium Yersinia pestis, a naturally occurring bacterium found in rodents. So, the Plague started off not as a human pathogen, but rather an animal pathogen. Meaning that the disease evolved. And in fact, the plague started off in Asia, not Europe. I've found a record stating about the Plague's existence at 17th century India, but that's about it since diseases in Asia weren't really recorded until the 17th century.
However, Y. pestis's genetic diversity and biogeography might suggest that it already existed in Northern China before any of the pandemics. And though not as popular as the Black Death, there were also outbreaks of the Plague in Asia, but as I said before, were not that well recorded. In 1331, there was an outbreak in the Yuan Empire that may have hastened the end of the Mongol rule over China. Then, the same disease killed over 90% of the Hebei Province's population (totaling over 5 million) three years later.
As of 1200, China had a total population of more than 120 million, but a 1393 census found only 65 million Chinese surviving.
The plague also destroyed Kipchak khan Janibeg's army while he was besieging the Genoese trading port of Kaffa (now Feodosiya) in Crimea (1347). So, he catapulted the corpses into the town to affect his enemies. From there, the disease was carried onto multiple places including Europe and England. And during a certain period of time, plague was introduced to Europe multiple times through trade routes because of disease-carrying fleas that were carried by rats.
So, you've got it mixed up. Asia was already affected LONG before the Europeans were.
