The paint on my ceiling is getting darker, like a shadow. It is occurring between the
Ceiling joists, in effect outlining where the ceiling joists are. In some areas dark circles are
Appearing about the size of a dime. There is an attic above with insulation in the ceiling.
What could be the cause?

It is a moisture / insulation problem. There is similar post to yours out there right now, read this when you have a chance.

https://www.askmehelpdesk.com/construction/celing-joist-showing-through-drywall-184987.html

I agree and also think you may not have a good moisture barrier in the ceiling. How thick is the insulation, where do you live and do you see a moisture barrier on the insulation?