Vendeur: Je vous en mets combien? Acheteur: Mettez-moi un kilo d'oignons.

I saw this dialogue in my textbook and I am wondering why don't we say "mettez-me un kilo d'oignons" instead.

My teacher said it's because "mettez-me" literally means put inside me which doesn't make sense. The common way to say "give me" is "donnez/mettez-moi".

Are mettre and donner exceptions that I have to memorize? Or is there a "verb + pronoun tonique" grammar that I should know?