Maxim never prematurely brought Dracula back to life. He simply found all the remains which then created a separate entity out from Maxims' dark desires and brought Castlevania back to the Earth realm. This entity is the one who kidnaps Liddy, taunts and fights Juste once prior to the end of the game, and uses the remains at the end of the game to make himself his own body. And there we have the 'Dracula Wraith'. Dracula himself was never in HoD.
I've got save-states of all the dialogue in HoD but it's going to be too many pics to post. But HoD is really ambiguous. Death and Maxim identify the "evil" Maxim as Dracula, while Evil Maxim identifies himself as some other spirit. Personally, I don't see Death serving someone who isn't Dracula.
Maxim: Ju- Juste...
Juste: Maxim! Is it the real you?
M: ... The other one... So you met him...
J: Yeah...
M :Oh... Dracula's power is great... soon he'll swallow me completely.
Here Maxim ID's the power as Dracula, and claims that he will consume Maxim's consciousness.
Juste: Ah, it's you!
Death : You know a man named... Maxim, I believe.
J: And, if I do?
D: That man... He's obtained something which contains Lord Dracula's power, has he not?
J: Could it have something to do with Dracula's relics?
D: Relics? I see, then it all adds up.
J: What do you mean?
D: Yes, that explains everything. You have my thanks. It's so simple... That man brought forth the castle.
J: What? There's no reason Maxim would do such a thing!
D: Perhaps not at first. But, if he obtained Lord Dracula's relics, then it's a different story. Two
spirits have received Dracula's power, and brought this castle into existence once again.
J: Two spirits?
D: At the moment two spirits dwell within Maxim. There is his own soul... The other is the evil spirit of
my lord, Dracula, which came from his relics.
J That's absurd.
D Still, I wonder why two castles have materialized... Dracula's spirit alone should have sought to call
forth the castle, but...
Here Death corroborates Maxim's tale about the evil spirit belonging to the count.
EM Oh? You're still alive, eh?
Juste Maxim! No, it's not him.
M Oh, so you've found me out, then?
J Who the devil are you?
M I am myself. Though, I'm not the same Maxim you know. I am the desires that were once sealed away in
this man. Since he obtained the relics of Dracula, another spirit took form within him. I am that
other. I don't know if he's even aware of me.
J Is abducting Lydie your work, then?
M Heh, heh, heh, obviously... That is of course my doing. But the fool has lost his memories.
He doesn't even know where he is right now! His memories will soon be revived. If we come to share those,
the woman will be mine.
J Bastard!
M If I perish, your dear friend will die along with me. Is that all right with you?
J Damn!
M You will die here, scum!
Yet here Evil Maxim identifies himself as some latent desire within Maxim, rather than the count. Personally I'm on Maxim and Death's side that the evil spirit is indeed Count Dracula and not Maxim's psyche.