House paint fell off the ceiling, how to repair?

The house was built 13 years ago. A few months ago, the plaster partially fell off the concrete ceiling. A few weeks ago, we applied a primer to the bare concrete ceiling and did nothing else. In the meantime, an acquaintance said that this was wrong. There are special primers specifically for concrete.

If this is the case: How should we proceed if we finally want to repair it?
Apply the correct primer over it? Which one?
Remove the other primer? How?

Thank you!

Priming coat is initially meant to reduce the absorbency of the substrate and, if necessary, to stabilize the substrate (for example in the case of sandy substrates). My layperson's opinion here is also that the priming coat was not helpful. However, I do not believe that it would need to be "removed" in any way, if that is even possible. Priming coat is supposed to penetrate into the material.

If the ceiling is therefore not very absorbent, you would need an adhesion primer that ensures the adhesion of non- or weakly absorbent substrates. There are also special concrete primers for this, just google it.