This chapter *is* confusing, but the takeaway from it is less the actual status of the woman Tsukishima loved, and moreso to show how deep Tsurumi's influence and willingness to manipulate the men around him is. The man from Sado either wasn't from Sado, or he was, but he was placed by Tsurumi either way, in order to get what he needed, and continues to need, out of Tsukishima. A man so loyal that he's willing to go to any length for him. A perfect second-in-command.
You can sort of see on tsukishima's expression when he says 'Oh... Is that so?' that he now is sure that she is dead. Whether killed by his fathers hand, or (my own personal belief) by Tsurumi/Tsurumi's men. To Tsukishima, he now realizes how far Tsurumi is willing to go in order to get what he wants, and Tsukishima resigns himself to that. He is Tsurumi's property, since he truly has nothing left to live for except for Tsurumi. And thats EXACTLY what Tsurumi wanted to happen. Maybe not exactly in the way that it did, but thats the spice of life for ya. You can never 100% predict what will happen.