Warbirds general manager Ed Taylor said he had been contacted by tourism operators who "expressed concern'', and he passed that on to US Air Force personnel in Christchurch, where the two jets were based.
They were here for a week before the airshow.
The tourism operators told him the jets were "flying low in our airspace'', and were concerned enough about safety issues to ring him.
When he contacted United States personnel, they said they would talk to the air crews.
The RNZAF would also have "shown them where they could and couldn't go and do that sort of flying''.
F-16 pilot Richard Smeeding said before the show the jet would "let me pull minus 3 to 9.9gs, go twice the speed of sound, rage through the mountains at 100ft fully loaded for war and all the time flying like an extension of my body.''
Fox Glacier helicopter pilots declined to talk on the record yesterday.