That to me seems like the wrong way to think about it. Of course most invasive species would come from Asia, because there was already free-flowing contact between North and South America, and there was already hundreds of years of contact between Europe and the Americas. East Asia was the place that was isolated from the Americas for the longest period of time.

I think a more interesting question is what kinds of organisms are treated as highly problematic invasive species in Asia from the Americas. That is, shouldn't we expect Asian species to be susceptible to novel American pathogens?

For example, it's famously known that diseases like small pox wiped out many Native American populations because they had no previous exposure to the disease. Perhaps less known is that it's widely hypothesized that a virulent strain of syphilis wrecked havoc in Europe after being brought back by sailors fro the Americas.