With 'Use shared settings' selected, also the minimap button position should be shared.
(Alternatively, you could add a 'Use global minimap position' option.)

Currently, when I rearrange my minimap buttons (which happens quite often) all my button positions are propagated to the other 17 toons – except for the Tome of Teleportation button. This is a bit pesky ;)

Thanks for considering, and thanks for the really useful addon

– Tom