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I don't think this is the subjunctive, I believe it is an example of the Portuguese personal infinitive: http://www.learn-portuguese-with-rafa.com/portuguese-personal-infinitive.html
Native speakers Paulenrique and lourenco.vidotto have been in touch. Lourenço confirmed that Duolingo's sentence uses the personal infinitive form of the verb. Paulo suggested a way of writing the sentence using the subjunctive instead: "Fique em/no seu quarto até que eu chegue/volte/venha".
I'm not sure I agree yet with making the correct answer dependent on material that will only be introduced much later in the course. I can understand an argument for surprising you with it up front, to let you know it's coming, or to make you curious enough to check other resources, but I'm just not sure this is a great way to introduce it.
The reason why it is used here is simply because it fits the situation and perhaps to avoid using the subjunctive. This article:
mentions that the personal infinitive is used in subordinate clauses introduced by certain prepositions, including "até" which matches this case.
Explaining the personal infinitive using English as a model seems to be impossible. In the English translation, until is a conjunction followed by a clause in the present tense not the infinitive: it would be very odd to say "until he arrive", for example.