Hi I bought one of these Omega fob watches yesterday at a car boot sale as it looked strange for an Omega.
I took it to a Vintage watch shop in Lymington (UK), and they concluded it to be a fake Omega probably made in the "far east." They said "all Omega movements are stamped with Omegas name."
The movement in mine, they said, was a "respectable" one, so I'm guessing yours will be too as they would have been made by the same people or company.
I still like it and will make a hook stand for it to hang from so I can see the time or look at the mechanics working away.
All the best and sorry for the bad news about it being genuin