"byen" is so misleading to Swedish people who think of "by" as "village" and then nope, it's a whole city in Norway.
When a third person or third persons of a sentence ‘owns’ the object, Norwegian uses a special reflexive form of the possessive pronoun. The forms ‘sin, si, sitt, sine’ are used for any third person subject. The reflexive possessive pronoun agrees with the noun’s gender and number.
In the sentence ‘De viser oss byen sin’ there is only one city but several people.
De viser oss byene sine. They have one city each. De viser oss byen deres = It is not their city.
Jeg viser deg min by.
Han viste meg sin by (sitt barn, si/sin bok).
De viste meg sin by, sitt barn, sin bok. (Two or more people with one city, one child, one book).
De viste meg sine hus, sine barn (they have one house each or they have many houses together).
De viste meg deres hus, by, barn (not their own house, city, children), Jeg viser deg min katt.
Jeg viser deg mine katter
Han viste meg sin katt.
Han viste meg sine katter.
Han viste meg hennes katter (He doesn’t own the cats).
Han viste meg dine katter. (your cats) Han viste meg deres katter (more than one person own the cats, they are not his, nor mine, nor yours).
I give you a lot of examples, maybe this will help.
Why isn't it "sine" since its plural, because we're talking about several ppl, and not just one?