This is just a guess from a learner like yourself, but it looks wrong to me. I would have said 'Attendez-moi, j'aurai fini dans trois minutes'.

C'est du registre familier.

Excuse my Frenglish. *le passé composé *elle n'a pas fini => être fini veut dire la mort! *son activité => Même si activité est un nom féminin, on aime pas deux voyelles qui se touchent :') There are two ways to use Passé composé: for actions that are definitely finished, and for passed actions that affect the present. True, there is a problem with that sentence, then. The sentence actually looks fine to me so often have I seen it. Admittedly, in speech, I would use Passé composé over using Futur antérieur. Bad on me; Futur antérieur is the proper way! It’s just the way people speak. Registre familier, comme Bertram a dit. It’s easier to say "J'ai fini" than "J'aurai fini," and it also sounds similar.

It's more an expression maybe means "in three minutes (not more)" but not generalise the correcte phrase is "Attendez-moi, j'aurai fini dans trois minutes" using "Futur antérieur"