Sorry for the OT question, but it is wood related...

As part of a window replacement project, I'm going to be removing my
aluminum storms. I expect that this will expose unpainted window
stops.

Should I prime the exterior stops before installing the windows and
caulking or is OK to wait until the caulk dries and then prime/paint?
I'm wondering if the bare wood will draw too much moisture out of the
caulk for it to cure properly.

Thanks!