The update is very small.. as in it just adds the AsicBoost feature. You can upgrade S9i as well. I confirm it works, I don't own an S9j but I assume it's the same.
you may say it works and it might, but it is not designed for the S9i or S9j - there have also been people who have reported it bricked their miners - I would suggest using the right firmware for the right S9 model. The exact same reason why the S9i and S9j had different versions prior to the asicboost version.