I have a 3 handle shower assembly and even when the diverter is turned all the way water still comes out of faucet!

Turn the water off to the valve and open up the diverter assembly. Change the washers and check the seat. If it's nicked or rough change it. Good luck, Tom

Hello what you may have to do is change your diverter or spout <same thing>it could be one of two type one with threads that turns off or a slip on which is held on by a screw at the very bottom and back of the spout allan key not sure of exact size bye