My shower diverter is controlled by a knob located between the hot and cold water knobs above the tub on the shower wall. I have replaced the diverter but water continues to flow from both the tub spout and the showerhead.

The diverter has two ways it seals, turning in and turning out. As you turn it in it inhibits water from going up to the shower. As you turn it out it inhibits water from going to the spout. Most of these type of diverters are not a 'positive seal' type. Some water passes by, typically very little though. It could be that your new part is defective, or it could be it is missing the large seal about the size of a quarter that seals the back side of the stem.