It's understandable for Alexander to feel shocked hearing what Ariana called him right there when they both maintained a 'formal' relationship with each other all this time, but he kept looking at her own in warm. She looks so small being in his arms like this.
"Am I dying?" Look like she is also confused by this situation as she starts talking nonsense before losing consciousness.
Realizing how hurt she was at that time, he gritted his teeth. He is here for other business but did not expect to witness something like this and what a nerve of her to think as if he will let her die when he holds her like this in his hands. He even got his hands dirty by killing the bastard who hurt her earlier.
Well, he wanted to curse and complain like that but he still has a right mind and knows why his daughter is behaving like this. He was never there as her father all this time, after all. There is no one to blame but himself.