The buds do appear at the leaf axils from the stem. I planted mine by seed in late March, and I started getting buds several weeks ago. Once they appear, they take a few weeks to grow and bloom. This is my first time growing moonflowers, and it looks like I'll get my first bloom in a few nights from now!

This is really a dumb question, but when you say "leaf axils" do you mean where the leaf stem connects to the main vine? I have little sprouty things coming out at that juncture, and am wondering whether these are the buds-to-be that you describe... I wasn't sure whether they were more leaves sprouting or buds...