I've seen Tiffany's use movements from a variety of high end makers. Of course, since Patek is the most famous (and highest value) everyone wants to assume that.
A watch like this NEEDS to be serviced; the precision of the parts can be quickly marred by attempting to run the parts with no oil (or worse, old/dirty oil). Get a good watchmaker to do this, and ask for lots of pics.
You should be able to contact Tiffany or Patek directly once you have these; if it's a patek, there may be a serial number on the dial-side of the plates.