Haka/Dominion vs. Shinobi Question

Could someone remind me what the sequence is when Haka defeats a Shinobi, and he has Dominion out?

Does Shinobi go on top of his deck, and then he draws?

Or does he draw and then put Shinobi on top of his deck?

And how does this work out if Haka also has Savage Mana out? What's the order of Shinobi-to-top-of-deck, drawing a card, and putting a card beneath SM?

Thanks!