Omega/Vulcain Pocket Watch

My take on this is that a closer examination of the underside of the dial might be needed. I would suggest that it is very unlikely that a watch would leave Omega with the Vulcain name stamped on the movement. Is this an Omega dial somehow grafted onto a donor movement? It is odd that an Omega dial would fit so well in a case marked for the Vulcain Watch Co. Or might this dial have been refinished many years ago, and the “Omega” name and symbol replacing an original dial marking?