"On the day that the Lord saved him" does not necessarily mean that he was saved in a single day from his enemies and from Sheol (the underworld), but rather that his salvation was equivalent to that of all his enemies combined. For anyone who attempted to harm a son of Israel, he was tougher than all the enemies of the world combined. Similarly, Samson said to them, "Swear to me that you will not harm me, otherwise you will be my enemy" (Judges 15:12), and they left him alone. Solomon also said, "A brother offended is more unyielding than a fortified city" (Proverbs 18:19).
David's Descent to the Edge of Sheol
Midrash Tehillim 18:6