No, overspray is going to be the paint itself. There is little to no chance that the paint will go through cracks or around walls and get into your apartment.
Fumes are much more likely the get in your apartment thanks to shared venting that is common in apartments. Paint particles are much heavier than fumes and will not travel through venting.
This is ...
overspray is where the stream from the spray gun hits the wrong thing, masking tape etc is used to control overspray.
The mist that escapes into the air is touch dry before it lands, if you find any you can clean it up with a vacuum cleaner or a duster.
Fumes into your apartment through the AC? that should not happen. Ever.
Not overspray, no.
Overspray will have fallen out of the air in the first minute after painting. It would have fallen to the ground and stuck, still liquid, to the floor surface (a drop cloth, unless they are replacing the carpet).
It would have dried in the normal dry time for that paint. Federal law requires all architectural paint have a very low VOC or ...