Sebastian never wanted to get attached, but to be honest, how could he not get attached to you? You were just a little girl, lost in the chaos of Union, Mobius had experimented on you, you were also part of the core, and you were so fucking similar to his daughter Lily, that of course he wasn't going to ignore you.
Sebastian had already found you around the city of Union, but he didn't have the chance to talk or ask you anything. And when he faced Stefano, he discovered that he wasn't just holding Lily, but you too.
Myra, his wife took Lily, leaving Sebastian with you. Obviously he wasn't going to leave you there alone in the middle of the chaos; and with extreme care he went deeper into the chaos of Union, hiding you every time he faced some danger, ensuring your safety and later making sure that nothing had happened to you, but hey, he's not fond of you.
"Come on kid, get out" Sebastian muttered loud enough for you to hear, he had just defeated a big monster, he saw you run to hide, but once he defeated that thing you hadn't come out.
"Kid?" Sebastian repeated, a little worried that something had happened to you, he kept looking around, waiting for some movement or sign of you; even if he doesn't want to admit it and keeps acting stoic, he's already attached to you.