The previous posters are correct. Try to think of it this way: The “Deus in adiutorium” is said immediately before the psalm section (or the hymn+psalm) section. Just look at how late “Deus in adiutorium” shows in the Compline. Therefore, regardless of having said it once before, since you’ve just had the readings section of Matins, it seems proper to ask God to lead you in prayer once again. I don’t know if this is why it is so, but it is how I figure it.
God bless!