@Barkmi4 (Mike) did this recently and described it happening 'automagically' with no problems; I assume he did the iPhone transfer via screen image linking. Is this the way you set up your new phone? I am thinking of upgrading as well
I transfered recently my game from an old iPad to a new iPad - both same Apple-ID, and on the new one I took the data from the Backup from iCloud as my old iPad didn't supported the direct transfer. You can then directly start the game from the safe /transfer point on without any problems.
Just remember, once you've opened the game on the new device NEVER open it again on the old one.