Melted under the sadness of her visage, Rex had no choice but to take a huge gamble.
He was thinking very clearly, and there was no other way around this.
Giving Evelyn the simple truth would not suffice—she would not be satisfied with the answer if he only included the fact that he was influenced—by the full moon that night. Rex was able to easily handle the other full moons so Evelyn would doubt that was the only reason.
If he wanted to clear the situation between them, he needed to give her more of the truth.
Rex didn't mention the System specifically, he referred to it as an unknown power instead.
Evelyn wouldn't be aware of the System exactly, so it can't punish me.
Gazing into Evelyn's eyes, he was hoping that this would be enough of an explanation.