No, you are using the correction factor in a wrong way.
If the 25A filter asks for a factor of 3 stops (or 8x), then you have to increase the exposure, either opening the diaphragm or slowing the shutter speed three steps. Always the change must be in the direction that increases exposure. In your example, the normal exposure is f8@1/125, then the correct exposure to be used with the filter is f8@1/15 or f2@1/125 (or any equivalent, like f4@1/60).
The "corrected" exposure you calculated f22@1/15 is exactly the same (in terms of exposure) as f8@1/125 because you decreased exposure with the diaphragm and increased it by the same amount using the shutter speed. In addition, you corrected twice, you need to correct three steps in total. In you example, you corrected six steps (three in the correct way and three in the opposite way).
MP