So I'm not sure that Hungary is overrepresented in science generally in the 20th century. They did have a group of fantastic physical-mathematical scientists that came of age within a few decades of each other. But this could be a fluke of small numbers as much as anything else. There were also many excellent scientists from Germany, France, Italy, England, Russia, Japan, and the United States, during this time. Of the Martians, von Neumann is perhaps the most scientifically and technologically important, the only one who Wigner considered a "genius."

The shared factor that the main "Martians" had in common was an excellent gymnasium (high school) education in then-cosmopolitan Budapest, and they came of age at a time in which the specific mathematical tools they each were taught were extremely useful for the emerging physics.

But I'm not sure we need to posit anything exceedingly special that a few of those people ended up being very successful, other than, again, the fact that at that time a highly-mathematical education was prized and available to them. Their flight from Europe with the rise of Nazism, at a time when their particular skills were of new value to the emerging American military effort, propelled them rapidly into positions of great importance, in some cases (like Teller) well beyond their scientific work up until that point. It was unusual circumstances that led this cohort of scientists to be important in a world outside of their country of birth, and to be so marked as "different." But we're talking about very small numbers here (five "Martians," plus a few more if you include economists and non-scientists), not a national trend.

The best comparative study of the "Martian" cohort, is Hargittai's Martians of Science.