In the zone proximal to ground zero, in the case of a ground explosion, within a few minutes extremely radioactive fallout will reach the ground and hence the contamination in this zone will be extremely high. This particles however will fall on a zone where probably no one has survived so that they will not create ulterior damage except, at a later time, in the eventuality of succor or reconstruction. Within one hour fallout will start to fall in the downwind areas so that whoever survived without serious damages the initial effects of the explosion will have reasonable time to provide to take shelter so as to avoid the contamination from the fallout, in any emergency-suitable location: a basement, a shop, a house of whatever available to afford initial screening from contact with the falling radioactive particles.

However, this does not mean that they have not already suffered some more or less serious irradiation from the gamma rays generated by the explosion. See following page:
Biological Response to Nuclear Radiation