The day Rex had approached Raphael's not to kill his mother in tears, Rex had also told him everything he and his mother had planned for the world, thinking that Raphael would join his and help his mother to escape her fate.
Rex was naïve and trusted his elder brother a little too much because of the love he had for him and Raphael wasn't ready to break that trust just yet as he loved his brother the same way and to think that the loved so dearly upheld such opposite beliefs to him broke his heart.
He felt pity for Rex at that point in time and to him, he was doing Rex a favor by killing the person who had successfully brainwashed him like so and if that wasn't a good enough reason, if Raphael denied himself of his execution duties, he would be executed alongside her as an accomplice of treason.