When a tub or shower faucet stem leaks when you turn on the water, it usually means that the packing nut needs to be tightened or that the packing material needs to be replaced. The packing nut is the nut closest to the top of the stem. You can tighten this nut without having to remove the stem. The packing material is under this nut. On diverter stems there may be an additional nylon seal that could also cause this problem if it is missing or damaged.
The little rubber washer at the bottom of the stem that you turned over keeps the faucet from dripping when the water is turned off (hot and cold stem) and it keeps the water from leaking out your tub spout when you are taking a shower (diverter stem).