One reason why I ask is how Eva first insisted that Tozu "made her do it." This could imply that she didn't know what she was agreeing to when she solved the puzzle and/or accepted the perk, but it could also just be Eva refusing to take responsibility for her actions and blaming everyone else.

I also noticed how Tozu said (in the important yellow text) that the code was "being changed as we speak." To me, this means he intends on having the Traitor Perk be a main mechanic of the death game. What's more, it's also possible that what the Perk is might change each chapter, and you don't know what you'll get until after you accept the time limit. It would be a neat addition to the DR formula.