If I understand correctly, you had two shafts, and I'm assuming they were different diameters, and your guy slid one inside of the other and welded them together? If this is the case, that is most likely your problem. Yes, it should have been done in a lathe or specialized driveshaft machine. I have seen many jobs done this way. Sometimes they work, but more often than not they have issues.
I would suggest you find a professional driveline shop in your area and at the very least see if they can balance the shaft. If it's a 2 pc, you will need to balance both pieces together.