That's our default translation, so sounds like a glitch/typo situation.

You always have the option of putting it behind the word it's modifying as well, but then that word needs to be changed to it's definite form:

"Høsten er årstiden deres".
OR "Høsten er deres årstid".

Which structure is used, "definite noun + possessive" or "possessive + indefinite noun" is technically always optional (the only times I'd argue that it isn't is in some set phrases, old sayings and the like), but when implying actual ownership of things we often say that placing the possessive first stresses that ownership; puts focus on it, while placing the possessive after the noun makes the ownership into a simple fact rather than the focus of the sentence.

When speaking rather than writing, you can stress the ownership by stressing the word itself, so the placement of the possessive becomes less important/effectual.

When the noun is placed after the possessive, it's left indefinite. If we were to switch them around, it would be "årstiden din", using the definite form of the noun. You can refer to my response to Loekild for a more elaborate explanation.

Note that it's the placement relative to the possessive that matters; whether it's toward the beginning or the end of the sentence is irrelevant.

You understand exactly what is meant.