It is not normal for any mower to leak fuel. It is a hazard and unsafe.
Strongly recommend you don't use the mower until the problem is repaired.
Since the leak is coming after the fuel valve, and only when it is turned ON, the leak could be in the tube [yellow] between the valve and the carburetor, where that tube is clamped on either end, or from a problem with the carburetor bowl area [green].
There is a float [pink] in the bottom of the carburetor that operates a valve to regulate fuel flow. If this float or valve are not working, either could be the source of the leak. There is a single bolt [purple] and sealing washer at the bottom of the carb that could be leaking if not sealed. Or, the bowl could be not fitted correctly or have a damaged gasket [blue].
If you are comfortable with DIY, it would be not difficult to repair, but if you don't want to fool with it, a Honda dealer can do the repairs for you.
Find A Honda Dealer