1) The moment Harrison arrives, you take him out of the house at once.
2) The moment Harrison arrives, you will take him out of the house at once.
Which one is correct?
As a matter of fact this is a future event (Harrison hasn't arrived yet), that's why I doubt between "you take him" and "you will take him".
Both are correct (the latter is more common, I think).
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Off-topic: If 'him' is Harrison, there's something wrong with the logic.
Harrison's arrival is complete once he is standing at the door of the house. Since he is not yet in the house, he can't be taken out of the house.
CJ