I admit I noticed when I looked at your page there was Kakarot bringing up Hellsing , But I have had this thought in my head for awhile honestly and nearly no one I talk to would be likily to do the ideal. Anyway you know this scene
https://www.youtube.com/watch?v=0F15nk6oGh4 is more or less stated by the manga maker as representing how awkward and sweet the two's bond has gotten as it had went into something akin to a cross of a father and daughter relationship mixed with a master and servant dynamic . So with everything considered I could see before that point Alucard do to showing a human side prior to then wants to help Seras get past the trouble her new vampiuric status and job is causing her aswell as old trauma that haunts her , aswell as a desire to make who he sired (Turned into a vampiette) be a more effective Vampire but doing what he can at first in ways that won't be out right noticed as his doing but as time goes on it evolves into him treating her like a child