Yeah it is something a lot of people experience, my thought on it personally is that running water kinda imitates the sounds made when you pee into a toilet so there is a subconscious link somewhere in the brain between the act of peeing and the sound of water running/falling), possibly wrong but who knows. Would be a curious but pointless experiment to raise some children from a potty training age to adult hood only every peeing in a way that is silent and see if the sound affects them the same way.
The one that I find is if my bladder is full and I do the dishes just having my hands in warm water for a period of time makes me "potty dance" a lot as the urge to go grows.