Learn Hardcore Japanese: datuizyo wo deta totan ni, tomodati ga onsenmanzyuu wo motte kita. - The moment I left the undressing room, my friend brought a steamed bun.

Good question. 出る is intransitive, but Japanese still often uses を with certain intransitive movement verbs to mark the place someone leaves, passes through, or moves along.

So in 脱衣所を出た, 脱衣所を means out of the changing room / leaving the changing room.

This use of を is common with verbs like:

家を出る = leave the house
バスを降りる = get off the bus
道を歩く = walk along the road
橋を渡る = cross the bridge

So this を is not marking a direct object in the usual English sense. It is marking the place associated with movement.

Why is it 出たとたんに and not 出るとたんに?

datsuijo o deta totan ni, tomodachi ga onsenmanjuu o motte kita.

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V-たとたん(に)

V-たら

V-たあとで