City-busters are always airbursts to maximize the blast wave and thermal pulse, and airbursts don't produce short-term fallout. All nukes, no matter where detonated, produce "short-term fallout" (as well as long term).
The Hiroshima and Nagasaki nukes were air bursts, and there was plenty of lethal fallout from them.
Air bursts don't produce as much as ground bursts, it's true, but there's still enough to kill many, many people.
Airbursts don't produce short-term fallout, i.e., that which precipitates out in two days or less, unless they are of such low yield that their fission by-products lack enough energy to be a significant hazard.