On the picture of the 2002 tank, there are two holes, but the upper left hole is the drain for spilled gas (and for rainwater).
The lower right hole is the vent hole, but it does not connect to the tank on the inside. It is meant to be sealed against the gas cap, which has its own internal vent connection to the tank's inside volume.
The 2003 tank picture shows one hole, which is the drain hole. The vent tube ends inside the tank at the very top, just below the gas cap. The gas cap does not have a vent - the tube connects to a charcoal can and vents through that. I think this is the California style tank and cap.
If you put a non-vented cap on a tank that needs the vented cap, then there is actually no vent on the tank at all, so it pulls a vacuum as the gas is used.
So, you can remedy this in one of the following ways:
1. Get a tank that matches the cap you have.
2. Get a cap that matches the tank you have
3. Add a tiny vent hole to the aluminum casting in the gas cap, and buy the correct rubber seal (cheap) from Honda to seal the gas cap body to the vent hole at the top of the tank.
I messed up when buying my own replacement tank a while ago, and found myself with the same problem you are having. I tried option 3 as it was the cheapest thing to try, and it has worked beautifully for me.