It is required, but why? There are a number of situations that require the subjunctive -- a couple for example -- Wish, Emotion, Doubt, Desire ...... In the text given in your query, seems to me that there is an element of doubt or emotion being expressed given that the brother needs to be watched while the beds are being made up. There is perhaps a concern that the brother may misbehave or come to some harm if not supervised.
Hope this helps.
Because it's a command
@Barbara: le temps que requires the subjunctive regardless of whether it is used in a command.
Je fais le petit-déjeuner le temps que tu fasses ton lit. -- I make breakfast by the time you make your bed.
Further to Chris's point, I would expect a command to involve the Impératif mood rather than the subjunctive mood.
Thanks to Jim, Barbara and Chris for their replies. le temps que je comprenne toutes les complexités de la langue française je serai un vieil homme
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