You caulk _after_ priming, not before. Caulk has more stick on paint than to bare wood. Any caulk can go over any primer. Your caulk is recommended to be topcoated with acrylic/latex rather than oil, which is understandable.
Casey

"You caulk _after_ priming, not before."

Not universal. I am using urethane caulk outdoors. The manufacturer says NOT to prime before application. I am sure that the other way around would work. My opinion is that they would rather guarantee sticking to their wide range of specified substrates than to a huge number of possible paint choices.

Your urethane is more of a sealant than a painter's caulk. Hence the great chasm of distinction. Few people want to caulk with urethane sealant prior to a paint job. It is a far more specialized product and not exactly germane to this topic.
Casey

I have to admit that it is kind of a pain compared to other materials. The biggest problem is that you need to wait a week to paint it. It is nice that you can paint it or not and it is supposed to be more durable than silicone or latex.

I don't see the chasm. The English definitions of caulk and sealant are very similar. What is the difference in your mind?

I would ditch the Kilz latex primer and go with the SW oil for starters. The slow dry oil is the only way to prep an exterior for painting. I never herad of a caulk REQUIRING a latex primer.