I don't think that this move is something Derrik did so he can brag about it to the jury it's all about the numbers, basically it is stupid to vote out Zach who is a bit of a loose cannon but is loyal, now Jocasta does not talk game to anyone beside Donny and even that is minimal, so the detonators/BS have no clue on what she would do if HOH. this explains what made Derrik flip.
Frankie and Caleb were in the beehive and Caleb was trying to find a way to justify voting out Zach if Zach actually was a sure-fire vote to keep all of them (the BS) there until the outsiders were out. Then he mentioned that IF Christine were to flip, the BS was screwed because they no longer had the numbers without Zach. Frankie was trying to reassure him that he didn't think Christine would betray them and that they were still voting out Zach because he was stirring up trouble. Caleb basically went with it, but kept voicing his reservations, asking if Frankie felt safer with Jocasta in the house, who no one knows how she'll vote or nominate, or Zach, who everyone knows how he'll vote and nominate.
At that point Derrick came in and Frankie invited him over to tell him what Caleb was worried about, the numbers game. A quick retell was told, and Derrick just said to not worry about it that they would talk later because he had to go take a shower. He goes to the bathroom and that's when Nicole pulls him up to the HoH and tells him that she's sketched out by Frankie because she "overheard" him tell Zach to go talk to Christine, which he did do. She basically then tells Derrick that Zach thinks he's safe and that if he were to be HoH, he would nominate Donny and Caleb, thereby solidifying in Derrick's mind that Zach is loyal to the Detonators.
Derrick goes down to the bathroom again, this time meets up with Cody, tells him what Caleb was worried about and what Nicole just told him. He mentions the numbers that were brought up by Caleb, and then goes something like "he's absolutely right!" At that point both Cody and Derrick begin to wonder if it actually is better to keep Zach.
So Caleb started the ball rolling, and Nicole unintentionally moved the ball faster.