Supra prices didn't actually 'go up' because of the movie. What happened was indirect and will not happen to NSX's, or at least it is not likely.
The import scene was growing and maturing. People in the early 90's who had modded civics now had 40k to blow on a car in the late 90's. The import scene continued to expand and aftermarket support did with it, and most importantly, the hunt for huge horsepower exploded. The Supra is a one of a kind. It's engine and drivetrain in general, can support basically bolt-on power to the limits of what you'll want to drive, street or track.
Why buy something else when it will save you money, frustration, and time to just buy the best powerplant? The 300zx can take 600rwhp, but it is more difficult for mechanics, has too much enginebay heat build up [nothing too crazy, just an issue], difficult to work on and was much more mass produced. I still love the cars and clean twin turbo versions are getting very rare. The FD was not reliable and was seen as much LESS reliable back when they were still catching on fire in parking lots than now. The VR4 is a cool looking pos, enough said. The Supra became known for its reliablility under massive strain. THAT'S why its prices went up. It was many converging factors. The movie, ofcourse, was marketed while this popularity was high, coincidently.
Without getting into too much detail, nsx's will never be seen with the 'potential' that supras do. However, they are one of the few very reliable import supercars which as tremedously helped their resale, even with a measely 276hp.