"He splashed water at me" - probably he brought his hand down hard on the surface of the water and made it splash up towards me.
"He splashed water on me" = either he poured the water out of a container in such a way that it splashed on a surface and so onto me; or he dropped something into the water which then splashed up onto me.
"He threw water at me" = he had the water in a container and by jerking the container the water was propelled at me.