Are Mister Handy purchases tied to a save?

I've enjoyed my experience with Fallout Shelter, and while I'm nearing completion with the game I'm considering buying a Mister Handy pack during the sales as a token of my enjoyment of the game.

While I'm aware that a deployed Mister Handy can't be moved between vaults, if I buy a pack of 5 of them, will I be able to deploy some of them in one vault and the rest in another?

I can only speak for the Android version, but unfortunately you can't transfer them. You purchase Mr Handy & lunchboxes from a specific vault, and so they are then tied into that vault and cannot be transferred.