An ability that triggers "whenever you surveil" triggers after you're done surveilling, even if you have fewer cards in your library than the number of cards you're instructed to surveil. It even triggers if you have no cards in your library.

If you surveil and put Blood Operative into your graveyard as you do so, its ability triggers once you've finished surveilling.

No player may take actions between the time you choose to pay 3 life and the time you return Blood Operative to your hand.