It sounds like a drain, but you need to rule out the water supply side as a possibility. You can remove the flanges or escutcheons around the valve handle and the shower heads. Use a flashlight, run the water and look for signs of a leak.
Assuming it is the drain, you are going to have to open up more ceiling. Water travels along subfloor and along joists, which is why you have it appearing in many places. The most likely leaks will be directly under the tub or shower drains. At these locations, there should be an opening in the subfloor, so if you open the ceiling at that spot, you should be able to see something.
One last idea: do these leaks appear during a shower or mostly connected with a bath? If anyone is in the habit of filling the tub above the overflow plate, there is a gasket here on the back of the tub. Check this out.