However, if you did not play DoN prior to Hur rescuing then your opponent does have the opportunity to respond to his own action first.
For reference, that was discussed and ruled in
this thread, which was also on Gifts.
The TL;DR of that part of thread: If an opponent moves to the battle phase without allowing an opportunity for opponents' dominants/abilities to be played before the end of the prep phase, the dominants/abilities may still be played. Further, the person who 'pushed the hero into battle' could choose a different hero to start the battle, if desired, as the prep phase hadn't actually ended yet. An opportunity to activate abilities and play dominants must be afforded all players in phases that they could be used.