Speaking strictly about setting an exposure (leaving out depth of field):
Pre digital, when 35mm, medium format and large format film was in normal use, you were often using a hand-held physical light meter - similar in function to your app I would imagine. I've never seen one that had a setting for the size of film you are using (I've been taking pictures since the 1980s, including medium format and large format photography, and with both antique and "modern" hand-held light meters).
The f-stop system should give us a set of numbers that don't need adjustment for film size (I'd almost say it was designed for that, but I can't find a reference). The best way to think of the f-stop is as a theoretical transmission of light on a unit area basis. So not the total amount of light sent to the film.
Note "theoretical" - real world lenses don't send 100% of the light hitting the front of the lens to the film (or sensor). The amount lost depends on the lens coatings, complexity of the internal design and build quality. But the loss is usually not that important for film still photography.
Your 35mm Nikon and Fujifilm camera both have on-board light meters that look through the lens and automatically compensate for the loss of light through the lens (in addition to perhaps doing other things, like compensating for light or dark subjects). The newer Fujifilm may be doing more compensating than the Nikon is capable of, which could make it better or worse as a light meter.
My advice would be to shoot a roll or two where you shoot three frames for each subject, one metered by the Fujifilmm, one by the Nikon and one by the app. Keep good notes about the settings for each frame. When you get the results back, you may see which metering technique works best -- or maybe even which works best for for specific types of shots. Make sure that both cameras are set to manual ISO and are using an ISO that matches that of your film and that the light doesn't change much between exposures.