I have a shower which has water coming out of the tub spout as well as the shower spout. I have a third valve with a knob that turns to left to turn the shower on. I have a plumber telling me that water is always going to come out of the tub spout when shower is on. I disagree. How can I fix this problem on my own...

Water should not come out of the spout while shower head is in use. If it does than you need to replace washer inside the diverter. It is same procedure as when you replacing washer at hot/cold water stem. Diverter has one extra plastic washer (white in color). This washer may be split. If so, replace it.

When you are finished with your shower and close water - yes, water will slowly drip out (pour out) from the shower stand pipe and through the spout. This is how faucets are designed...

The diverter stem can be remove and rebuilt or replaced just like the hot or cold water valve stem.

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What I think Milo means about when you finish your shower is that if you had a diverter valve on the tub spout, when the water is turned off, the diverter (on the tub spout) will automatically open and switch back to tub filling.