"Déménage" is in the present tense. Your verb (is going to move out) is not exactly in the future tense: the future for "to move" is "will move", not "is going...".

Most people say "mon frère déménage dans trois mois" instead of "mon frère déménagera dans trois mois" because the future tense implies that the action (moving) depends on (is contingent on, to use a fancy phrase) another event (like beginning of university), or the person speaking is making a prediction or a promise.

For example: "mon frère déménagera dans trois mois lorsqu'il aura fini ses études" (my brother will move out of the house when he finishes school) or "je déménagerai demain" (I will move tomorrow).

If your sentence were "my brother will move next year", then it would be "mon frère déménagera l'année prochaine".

Ref: Native fluency in both languages.