Does the first missile kill the targets? Do the launchers know, for sure, before they launch the second?

Or are they launching two for redundancy, like often happens in military situations? Planes and missiles can break down or get shot down. If you want the target destroyed, you send more than one.

Actually, I agree about the timing if you're right that it was minutes apart (which I haven't confirmed). Hate to say it this way, but they did kill the initial targets, not first responders. The targets were school children maybe negligently flagged as military, but that's separate from the double-tap strategy itself.

It is different when they wait longer, which you mentioned was happening in Gaza. IDF waited for paramedics to arrive before striking again.