It should be AFTER damage step, cause it have to send the destroyed monster to the graveyard, and sending the destroyed monster to the graveyard is a bit after damage calculations.
For example, if Hydrogeddon destroys a face-down Night Assailant or Old Vindictive Magician, Hydrogeddon cannot pull out another Hydrogeddon if the player uses it's effect to destroy that Hydrogeddon.
But I think it'll be different for Newdoria, since both effects are activated at the same time. I heard something like you can put the chain of order so you can activate Hydrogeddon first and then Newdoria later. (Cause Newdoria is mandatory while Hydrogeddon is optional.)
But I'm not a judge. You should wait till one of the judges answers your question also. I might be wrong.