And how similar or different were these effects to the ones Europe experienced?
I do know a little about its effects in Asia, something to do with the Mongols throwing diseased corpses and a little about the bacteria in China. But that’s about it, I’m not super familiar with this period of history at any rate.
There is always more to be said, of course, but a long response to this question can be found here, in our FAQ. It covers the Black Death in China, the Middle East and India, and looks at the currently popular academic theory that the disease that devastated Europe in the 1340s originated near the Caspian Sea and may not have reached China at all.
Unfortunately, there is no conclusive evidence that "millions" died in Asia, excluding the Middle East, at all, much less surviving contemporary sources that would allow us to make rough estimates as to how many millions – the types of records that make this possible, to a degree, in Europe, just don't exist for other societies, and even the European records are so fragmentary and inexact that estimates have varied over the decades from 25% of total population up to the current estimate, based on both historical sources and knowledge of epidemiology, of as many as 60%.
As for the stories you have heard about Mongols flinging diseased corpses into besieged cities, these concern Kaffa, in the Crimea, a Genoese outpost in the Black Sea which was besieged in 1346 by the Golden Horde, a Mongol successor state located in what is now southern Russia. It is generally accepted that Italians fleeing from this siege were indeed the primary carriers of the disease as it moved into Europe, but, if anything, the suggestion that the Golden Horde was the first polity known for certain to have been struck by the Black Death adds weight to the idea that the disease may have originated around the Caspian and not – as has traditionally been assumed – in China.