"Nem! Köréjük nem!"

Translation: No! Not around them!

[SedatKlc]

normally we add nem before the word. why is after?

[vvsey]

The word, what word? The word that we are negating. But the word (probably a verb) that we are negating is missing from the sentence. It would be understood from context, from the preceding sentences. I think a closer translation would be "Around them, no!"
Q: Are you going to sit down around them?
A: No! Around them, no (, we are not going to sit down around them)!

In Hungarian: "Nem! Köréjük nem (ülünk le)!"

But you can also say "Nem köréjük (, hanem a fa köré)!" - Not around them (but around the tree).