Is it weird that this turned into a normal situation instead of a bloodbath?
Not really. after all, Fujio and sakurai had ALREADY gone through that when Hana told them they were dating, and he was the boy that she liked.
Fujio already had the moment of being pissed at him to hell and back, and being jealous. He starts mad because he doesn't know what happened to his daughter and wants to make sure nothing weird is going on, then when he notices how Sakurai is meeting him, he notices that everything is fine and she's being taken care of properly, so he calms down and decides to talk normally.
He knows Sakurai is serious about the relationship and wants to care for Hana, and already had to fight his feelings once, so him acting properly mature feels both natural and like a great show of his development.
It's just a very nice piece of writing.