Terminus as an instant?
Yes, your opponent can do this, as long as the Terminus is the first card drawn that turn. It doesn't matter whose turn it is, or that Terminus is a sorcery, Miracle will trigger if it is the first card drawn on by that player on that turn.

From the Avacyn Restored Mechanics article:


  As you draw an instant or sorcery with miracle, if it's the first card you've drawn this turn, you can immediately reveal it. When you do so, you may cast it for its miracle cost. It doesn't matter whether it's an instant or sorcery; if you choose to cast it, you do so right away, even if it's at a time (such as your draw step) when you couldn't normally cast it.


And the CR:


  702.93a Miracle is a static ability linked to a triggered ability (see rule 603.10). "Miracle [cost]" means "You may reveal this card from your hand as you draw it if it's the first card you've drawn this turn. When you reveal this card this way, you may cast it by paying [cost] rather than its mana cost."