I am sure Chief mentions at one point that Atriox came for the Weapon.
But she had already been deployed to Zeta Halo since we find her there and she was able to lock Cortana down. So she can’t have been aboard the Infinity. Since Atriox plan, presumably, relied on timing all of this so that he didn’t screw up the plan to trap Cortana; surely he’d have been aware she wouldn’t be on the Infinity? So why go there?
Did he really just board the Infinity to kill Chief and spite Cortana? Obviously the Infinity would be a problem if he intended to take the Halo ring at that point so he could have been just taking them out whilst he still could.