Yes, Kilz is to prepare the wall for paint. It is Prime's the surface there by making the paint more adaptable. It is also suppose to kill fungus, mold and mildew that maybe on the base board thus ensuring the paint to stick and last.
Yes that is a great primer. But you must let it dry completely. If you laid it on thick then at least 48 hours. Check the inner corners with you finger nail for any soft spots. If it's not very dry then you won't get complete adhesion.