If this is how it works and you can just keep reusing the same FB account, why even bother using a dummy FB acount? Can't you reroll until you get something you like, and then reuse your real FB account?
You can not. The first game you link with you "dummy" account is the one that overwrites all of your subsequent re-rolls, and starts a fresh game when you logout. If you were to use just one Facebook account, when you finally obtained your desired roll, if you were to link it to the Facebook account you linked all of the previous re-rolls to, it would immediately overwrite and replace your current account with the one you had when you first linked a game to that particular Facebook account.
Basically:
First account re-roll you get Vivi. You link it to Facebook #1, log out, and start a new account.
Second account re-roll you get Shantotto. You link it to Facebook #1, which replaces your Shantotto account with the one with Vivi. You logout and then start over again.
Let's say, for instance, or your third re-roll you got Exdeath (you lucky bastard). If you were to link it to Facebook #1, you'd lose it since you would just revert your account back to the one with Vivi. In order you keep it, you would have to link it to a new Facebook account (Facebook #2), one that doesn't already have a game tied to it.
I hope that makes sense.