Due to the rotation of the Earth, the irradiated zone from nuclear explosions stretched far to the west of ground zero. Was the US aware of this before they dropped the bombs, and did they take advantage of that knowledge to maximize damage? Additionally, are there accounts of communities in mainland Asia that were affected by radiation?
I think you are confused — the rotation of the Earth is not a significant factor in how radioactive contamination is spread, unless you're referring to the fact that prevailing winds tend to be west-to-east for northern latitudes. The contamination spreads wherever the wind is blowing, which can have general trends (prevailing winds) but on any given day it can be any direction at all.
In any event, the bombings of Hiroshima and Nagasaki were high air-bursts, and as such had very little local contamination. There was not only no significant contamination at these sites, but none elsewhere in Japan, much less other Asian countries. Contamination was not a factor in US targeting of the cities.
Hiroshima's aiming point was more or less in the dead center of the city. Nagasaki's is less clear — there are some records that indicate that the actual aiming point was in the eastern part of the city (the denser more industrial part), but the official aiming point was said to be in the south-west part (but the actual bomb went off several miles north of that, so the actual detonation was more northwest).