First thing I'd do is take the handle and eschution off the tub/shower control and look behind to see if I could see what was going on. YOu have to determine if it is leaking from water finding its way from inside the shower out, or from a leak behind the wall. This may help you make that determination. Another thing you could do is fill the tub. Let it sit. See if you have any leaks. If not, then drain the tub, then look for leaks. This would help isolate it between drainage system and supply system.
It is also possible that the tub spout seal isn't great, and when you pull up the diverter, that pressure in the tub spout is allowing some water to leak back along the spout's pipe, back into the wall. This could be a problem with the pipe or the spout.
Generally, unless you have galvanized pipes, after a long time, leaks aren't that common in the supply piping...could happen, though. There have been some problems ove rthe years with some plastic piping systems, and this may be the tip of the iceburg leading to a whole house repipe, but hopefully, is an isolated problem easily fixed.