We see in Rose that he's only recently regenerated.
We don't. We only see him mention in passing about his new appearence, which for all intents and purposes could've been recent - not recent like just a few days ago, but recent as in, for a while now.
Really, I've never really bought into that specific assumption he'd just regenerated based on the mirror thing. He seemed quite together in ways no Doctor has been since Tom Baker, and that might've been because Tom Baker's Fourth came to be with the assistance of that ethereal whats-you-call-him Time Lord. The Fifth, Sixth, Seventh, Eighth (especially him), and even Tenth and Eleventh (though the least of all, probably) had a good adjustment periods before they settled to their new selves.
The Wormhole wrote:
My personal interpretation is that the Eighth Doctor was involved when the Time War began, and that he was trying to be good, indeed it could have been him who tried to save Davros from the Nightmare Child as mentioned in The Stolen Earth. Then when he regenerated and became Hurt, he could have become ruthless and decidedly un-Doctor like until eventually he regenerated becoming Eccleston who finally decided to bring the Time War to an end.
If Hurt's Doctor HAS to be involved in the Time War, then I hope what you've said is done. Perhaps he did something nasty that had nothing to do with the Daleks or the Time Lords, and that action comes to bite the Tenth and Eleventh Doctors in the "present".