I would not worry about the pump running with the switch on accessory and not when the key is out of the switch. I may be there is another relay powering up instead of the pump circuit going directly to the battery. My knowledge of Honda's is not that specific so for the time being don't get to concerned with that.
I have seen a leaky windshield dump water on the ECU and fire up the pump and the ground circuit to the injectors in a 300 ZX. When the car was towed to us 4 gallons of fuel had been pumped into the engine and it was liquid locked with fuel in the cylinders and the cranckcase was full of gas!
regards
Mech
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