I checked the '11 g4 cap; the overfill exit hole is outside the cap gasket seat area. That is the only hole.
edit: after re-reading your original post about the two holes UNDER the cap, I checked my above oem cap and it has one hole under the cap BUT still inside the gasket area that must seat upon the top of the filler cap. Has to be same with your new cap but either the gasket is missing or wrong size. Hope this helps.
When you open up the standard cap you can see a small vent hole on the right hand side which has a rubber seal.
But when you unbolt the cap there is an overflow hole underneath on the left hand side so it can drain when the bike is on the side stand.
I think my main seal isnt quite sealing on the quick release cap i have which i can solve with a thicker seal.
The issue i have is what do i do with the vent hole?
If i block it the tank will pressurise but if leave it surely fuel will leak out of it when the tank is full?
After market items seem to just come with a seal for the main refuling hole and nothing at all for the breather hole