When you attach Captured by the Consulate to an opponent’s creature, you still control Captured by the Consulate. Its last ability triggers whenever your opponents cast a spell with a single target, not when an opponent of the creature’s controller casts a spell with a single target.

When a player casts an Aura spell, it targets the creature that it will enchant and may cause Captured by the Consulate’s last ability to trigger.

If a spell has multiple targets, it doesn’t have a single target even if the same object is chosen for each of those targets.

If the spell can’t target the enchanted creature, its target remains unchanged.

If there is more than one Captured by the Consulate on the battlefield, the triggered ability of each one will change the target if able. The last one to resolve determines what that spell finally targets. If one player controls more than one Capture by the Consulate, he or she chooses the order in which they resolve. If multiple players control those Auras, the first player among them in turn order (starting with the player whose turn it is now) is the one whose triggered ability resolves last.

There are many important moments in the story, but the most crucial—called “story spotlights”—are shown on cards. You can read more about these events in the official Magic fiction at http://www.mtgstory.com.