When someone says they just installed a new shower diverter, but now they have a leak downstairs, that is a pretty good indication that the diverter installation didn’t go so well.
If you were to remove the tub spout diverter you would likely see just a bare pipe (although some are screwed onto threads). With the bare pipe type installation in particular, there is an o-ring that seals out water from exiting the rear of the tub spout diverter. Want to guess where the water goes when it exits? It goes into the wall. So I’m guessing that the cause of the leak has to do with the connection where the spout meets the pipe.
For the bare pipe connection, it may be that the o-ring has twisted or is torn. There is a lot of pressure on that part, and it is smart to remove it and inspect it. Use an allen wrench and loosen the set screw underneath the spout. Then you can pull it off. If the rubber is damaged, replace it. When you reinstall the tub spout, you can try some liquid soap on the o-ring to help it slide along the pipe without twisting. When you have the spout in the right location, tighten the set screw. Leaks are never good and can be pricey if not taken care of in a timely manner. Give Las Vegas Handyman a call if you have any questions or suspect a plumbing leak.