If I am already rolling to beat the creature's Armour Class, where does the Intelligence vs. Reflex check come into play, in (let's say) the move Fire Burst?
The attack specified by each power determines what kind of an attack roll you make against the target(s) of the power. Not every attack targets AC. Many powers target one of the three other defenses: Reflex, Will or Fortitude.
If a power you're using specifies that the attack is Intelligence vs Reflex, then you roll a d20 and add your intelligence modifier. The power hits the target if the result is at least the target's Reflex score. The same logic holds for any combination of attribute and defense.
For many powers, you don't roll against armor class at all. You roll an Intelligence attack against the enemy's Reflex defense. You may want to re-read the PHB section on attacking to clear up some confusion you might have as to how attack powers work. Not all attacks have to hit AC.