See if this works- once you have reinstalled, updated (at your own risk, since the update seems on some devices to insure total game crash on start up) - and if as you said, you had your vaults saved.... You will see that it looks as though you must start new vaults. (The 3 new vault slots where your vaults once were) Try tapping the cloud button beside each empty slot, and see if your vaults (vault numbers) appear?
I went through this a couple of times, and had to play with some settings on my iPad, but the "new vault" slots were replaced with my saved vaults ...
The directions and explanations given by Bethesda for the reinstall/reboot/cloud save and retrieve should be better, because in some cases vaults do actually wind up getting deleted by using the very steps they suggest. Good luck!