There are two critical steps in prepping kitchen walls.
Clean and degloss
Cleaning is critical: TSP or TSP substitute.
Deglossing: either light sanding (120 grit) or a chemical deglosser
Once a surface is deglossed, it should be primed, especially if going from one paint type to another.
A deglossed oil undercoat can be primed with a latex primer. Either oil or latex can then be used as a topcoat.
A deglossed oil undercoat can be primed with a oil primer. Either oil or latex can then be used as a topcoat.
It is better to stick within families of paint types, if you can, but going back and forth between types is possible with primers.
At this stage in coating, I'd let everything dry for a week, then sand lightly. If the previous layers are adhering, then proceed with latex primer, latex topcoat.
If,, however, they are sloughing or chipping or you can easily pull a layer off if you leave painters tape on overnight (and then pull it off), then you must sand down to the last well adhered layer and then repaint. Good luck.
If the prior owner used caulk, and they were really dumb and didn't use paintable latex caulk, then its possible that this would be the result.
Regardless, obviously the paint isn't taking properly here - so yes, the answer here is get a quart of primer go over the edges with a brush, let it dry, and redo the corners.
Best Answer
It would appear to be that way. There should be a layer of primer. If they did I am sure you would have seen some white on the other side instead of just yellow.