Why does my shower head drip when the tub faucet is on?
What did you use to connect your tub spout?

I plumbed my bathroom with Pex and was heavily cautioned NOT to use Pex to run from the main valve to the tub spout because it would create exactly the issue your describing.

Since the inner diameter of Pex is slightly less than regular copper (or threaded brass fittings, which is what I used) it will create a slight flow restriction to the tub spout and (inadvertently) divert it to the shower head.

Just a thought...