The WT CJ4 has always been spot on for me. While simple for a jet, it can definitely be a handful when you’re accustomed to smaller GA planes. But for me, the AP has always done what I told it. When it hasn’t, it was usually me that messed something up.
Now that said, I would try doing the ILS at various airports and perhaps try the one in question with a different plane to confirm whether or not it could be an issue with the 3rd party airport you’ve got.