Sword of Spirit
Legend
By the time they react, they do know your party is there. As per Shield, you take the reaction when you are hit (or targeted by Magic Missile, which sets off your Spidey-senses). If you get them while they're still surprised they can't do that.
The assassin's party attack from an ambush. No one in the other group has sufficiently high passive perception to notice them, and therefore they are all surprised. Everyone rolls initiative. The other group (which might only be a single creature) rolls higher and goes first, followed by the assassin, followed by the rest of his party.
All of the opponents take their turns (doing nothing) and become able to react (ie, no longer surprised) by the time the assassin's turn comes up. Since none of the assassin's party has given away their presence, the other group shouldn't even know there is anyone to be fighting, much less have already become "unsurprised," but because of how initiative rolled the assassin has a nerfed assassinate in this situation. That's the situation I'm addressing.