It is simple if you think about it like this: Reflected meters place whatever they are pointed at as a middle gray. Incident meters place middle gray as middle gray. That means that dark things end up dark, middle-toned things end up middle toned, and light things end up light. With a reflected meter, whatever it is pointed at ends up as a middle tone, regardless of how dark or light it is in reality.
The dome needs to be pointed at the right thing, of course.
And no; assuming the same value is used for middle gray with both meters, a gray card reading should not match an incident reading. You should have to open up 1/2 to 2/3 of a stop from a gray card reading to match an incident reading. And the gray card takes the place of the dome, so should be placed where you would place the dome.
Assuming both meters are calibrated properly, I would trust the incident. It is far more likely that the reflected meter is telling you to underexpose than it is likely that the incident meter is telling you to overexpose.