'I know you can hear me... when I say never, I mean truly never', Rex thought inside his head.
Since whoever his other side was is also inside of him, it's almost certain that just like Devo this other side of him can also read or hear his mind. It pisses him off when he troubles himself to give an antidote for the man just to be killed later.
Not only that, the beggar is just an innocent citizen and that made it way worse.
Evelyn saw the furious look on Rex's face that clearly shows that he was angry, she also curses herself a bit for not realizing sooner that it was not Rex when he called her not by her actual name.
Back when Rex woke up, he called Adhara the Female Alpha, and Evelyn Luna.
From that alone, she should've immediately stopped him knowing that Rex never called her that. But she only finds it odd instead which leads to the other Rex killing this innocent beggar.