If you wanted to prime the ceiling for the purpose of blocking moisture that is a good idea. You can still prime it as long as the paint he used is not peeling from the surface. Or you could buy better paint made for bathrooms and places that may get moisture from steamy showers.
If you try to lay a topcoat over an inconsistent surface, the inconsistencies will "print through" and give an inconsistent result.
Look at what you have there, you have a dog's breakfast of colors and surfaces. Different colors, stripper-etched vs normal, stains, and whatever that caulking or filling material is. (you're in trouble if it's ...
Primer is generally used for one or more of these reasons. If they apply, use it. If you're unsure, use it.
Save cost (cheap sealing and color/texture uniformity coat)
Improve adhesion over glossy or dirty surfaces