Don't know about the USA, but in the UK and most of Europe, an active, registered DZ, or an area NOTAM'd as a temporary DZ (example, for a display) must not have props or rotors turning on the ground whilst a drop is in progress or about to exit, and no overflying within a radius of three miles of the center of the field. The exceptions to the latter are for the para-dropping aircraft returning to land after the jumpers have exited, and, of course, high-flying traffic, both of which would not cause conflict.
That said, I was in freefall once over a registered DZ, back in 1984, passing through about 3,000 feet IIRC, when I saw a rapidly approaching dot, which very quickly developed into a Buccaneer, which passed directly below me, slap over the center of the DZ, below 1,000 feet !!
I believe the crew got a sever bollocking!