Could this be only be applicable if one also sets the aperture on the camera for accurate shooting aperture in exif?
Yes, but this doesn’t seem to be a problem exclusive to the Shoten adapter; it also appears to affect the Neweer and Funmount adapters.
It probably has something to do with how the aperture behaves on Nikkor Z lenses (and manual-focus Nikkor lenses fitted with Dandelion): from f/1 to f/5.6, the aperture blades close in line with the setting on the camera’s control dial. If a smaller aperture is set on the camera, the aperture blades on the lens stay at 5.6 and only close at the very moment the shutter is released.
As Richard has already suspected, the problem with the Neweer/Funmount/Shoten adapters only occurs when an aperture smaller than f/5.6 is set on both the camera and the lens. The camera seems to think that, with an aperture of 11 set on the body, the size of the blades corresponds to an aperture of 5.6 on the lens (with manual lenses, however, the aperture does indeed close to the value of 11).
With these adapters, it is therefore no problem to shoot from wide open to f/5.6 AND to set the corresponding value on the camera’s control dial for correct EXIF data.
Photographing with apertures from f/6.3 down to the smallest aperture is also no problem, as long as the control dial remains set to a maximum of f/5.6 (the EXIF entry is then no longer correct, but I suppose you have to live with that).
Side note: with the Voigtländer lenses for Nikon Z, everything works as it should; however, the camera’s control dial has no function there either.