I was running a session a few days ago for some high-level characters and in the palace vault they found themselves an Efreeti Bottle. I rolled for the efreeti's response to being released per the DMG, and wouldn't you know it, they got the result:
91-00: The efreeti can cast the wish spell three times for you. It disappears when it grants the final wish or after 1 hour, and the bottle loses its magic.
The efreeti pops out and reluctantly greets them and spells out what they've found. After the excitement subsides, the predictable line of thinking comes about and they discuss wishing for more wishes, which I shoot down as cosmic law dictates this and that, and we all understandingly nod our heads and move on.
But as I reread the section on the Efreeti Bottle and skimmed through the Efreeti in the Monster Manual, there's really nothing per RAW that would prevent a character from making a wish like "I wish you would grant me 10 more wishes" immediately followed by something like "I wish you would disappear after 1 year instead of 1 hour".
So if a character gets a hold of an Efreeti Bottle and essentially wishes for more wishes, per RAW, does it work?
Per RAW the DM decides about wishes.
You did the right thing. The PHB treatment of wish is pretty clear about - beyond the duplication of other spells - wish being finally adjudicated by the DM. The DMG does not counter that with any further guidance on the results of wishes. This makes it simplest to treat any wish as an iteration of the wish spell.
It is often simpler for the DM to advise the player "it doesn't work that way, try another approach" than to spend the effort to dream up whatever goes wrong. On the other hand, sometimes dreaming up what goes wrong can result in hilarity and fun at the table.
As a DM, go with what works best for your table.
For a darker feel, consider the trope that has grown up around the 1902 short story The Monkey's Paw - each wish granted comes with a hellish price. (Thank you to @ChrisFernandez)
As @guildsbounty points out, older editions encouraged the DM to gleefully corrupt any loopholes in a wish phrased by a player. An Efreeti that knew you were trying to manipulate it would find a loophole in your phrasing.
"I wish you would grant me 100 wishes" could easily be corrupted into "Here, let me pick the 100 most demented, destructive wishes I have ever granted for anyone, and grant them for you...all at once."
The Efreeti has technically lived up to the bargain - he granted you 100 wishes, just not 100 wishes of your choice.