It is not at all uncommon if you have aleak for the water to travel a little bit - to the next joint or whatever, which breaks up the flow and causes it to drip off of the pipe. Sounds like you need to dig into this and figure out what and how this is leaking. If it is old, it could be a corroded pipe, if new, it could be a faulty installation, or defective part. Is there or has there been any water leaking out on the floor? It might be that, and not the plumbing. It could also leak from a bad caulk joint or a broken grout line in the tile. Especially if the tub is not level, water can pool and leak into the wall. The caulk might have failed, and just now start to reveal that fault. Lots of possibilities. If there aren't any visible grout or caulk problems, you'll probably have to tear out part of the ceiling and take a look to see what's happening. Note, I'm not a pro.