I have discovered the next problem. Below RMMapViewDelegate method is not called correctly when RMPath is available.
That is enough to remove the path and tapOnMarker starts work well. Does anyone know how it may be resolved?
I've got it solved in a bit weird way. You just have to add path layer before adding the markers.
Alternatively, give your markers a zPosition property greater than the path's. This will layer them above the paths, regardless of the order you draw them in.