The pilots were "briefed on aviation rules here", and no further action will be taken by the Civil Aviation Authority over the events.
The CAA has released more information to the Otago Daily Times on what it said were two reported incidents regarding aircraft during the week of the air show.
A spokeswoman said one of them, on March 28, "concerned the aircraft being flown low and in close proximity to a helicopter near the Franz Josef glacier".
"The other, on March 29, concerned F-16 aircraft being flown low and in close proximity to three parachutists near the Fox Glacier.
"In both incidents the F-16 pilots were not in radio contact, so other aircraft did not know they were in the area."
The F-16 pilots were made aware of the rules and there were no more occurrence.
As a result of CAA looking into the incidents, the pilots were briefed on aviation rules here.
Asked if action would be taken on the two complaints, the spokeswoman said the pilots had left New Zealand, "and we don't intend to take further action".
A New Zealand Defence Force spokesman said while the United States Air Force pilots were in New Zealand at the invitation of the organisers of Warbirds Over Wanaka, the Royal New Zealand Air Force did provide a briefing on local flying procedures.
"After the pilots were made aware of complaints about low flying, there were no further incidents."
