Yep - either your fingerboard is resonating (not sure if you meant it happens from a pizz'd more, or slapped) OR you could be having an issue with the wire lead from the pickup itself. I find that its a very 'hard' (or not as pliable as the coating on the wing pickup) plastic they use, and mine used to resonate so bad it actually used to feedback itself! It sound like this might be what's happening to yours.
The solution is easy - a couple of small pieces of foam strategically placed under the fingerboard, and then you tape the wire to the foam bits. Two is all you need really - plus the one for running the lead through the bridge heart. Don't stick the first piece too close to the pickup element, I did that once and it tends to lift the pickup away from the fingerboard I'd the foam is thick enough.