It's the aperture! It took me a while to figure this out and signed up to the forum just to post this, as it's hard to find answers on the web.
Basically, I believe what is happening is that the firmware inside the lens is making an "aperture shift" decision during zooming. For example, I'm using the 18-55mm 2.8-4.0.... which of course (and we all just accept this) has an aperture change during it's zoom range. I believe that somehow the Fuji firmware is making this "gradual adjustment" to compensate for optics during the zoom process which is resulting in the "shifts" during zoom.
Workaround: Shoot wide open. For example, if I shoot at F2.8, the problem disappears completely. Even stopping down by a single stop makes it come back with a vengeance.
This is, of course, a terrible flaw. However, using the ISO and Shutter speed combined, you can at least (USUALLY) obtain a proper exposure. At least it's better than the other way around.... with a narrow depth of field at least you can still pull focus effectively.
I don't use my Fuji for video much. Thank goodness, because this is a real limitation. I hope they fix it. This is awful really.
