Hi, I have a brand new American Standard tub and shower one valve faucet and when the tub water is running the shower is running water also. Any Idea what might be the problem.

Do you have push-button diverter valve on top of your tub-spout ?

Yes, I even took the tub-spout off so there would be no water restrictions.

Take the valve back and get another. I prefer Moen but its up to you, I think you got a lemon.