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Wouldn’t there be nineteen more, not nine?
No it works like this whatever the person rolled in this case a 10 means they have 10 wishes each granted by a different genie with a different theme personality and power set/level.
Its only 1 roll per person and the genies cannot undo the work of other genies except for the last Genie who can't do anything but can undo any one wish/magical effect/past event/underlying law of physics.
Also the 20 Genie is all powerful and can do anything with its wish the other genies are more limited.