It very logical. No leak when you don’t open the bath/shower faucet. Therefore, there is no leak up to the shower/faucet diverter valve. When you open the daucet there is a leak. Ergo, there is a leak in the outflow from the valve to the tube faucet or shower head, and/or there is a leak from the tube/shower drain or the tub surround. To dertermine which it is try to get a hose up to the tub/shower and run water into the tub and into the drain. If you detect a leak, then you know it is from the drain or the tub surround, since you haven’t sent water into the diverter outlet pipes. The advantage of using a hose is that you can fill the shower pan/tub and check for leaks, and you can spary water on the walls of the shower/tub to see if a leak occurs then.
Troubleshooting plumbing is a matter of knowing how the systems work and very simple logic.
NtP