Some other ideas
If a spy is caught it should also have a % chance to tell you who they belong to, with deception as well.
60% - Interrogation failed, unknown civ.
39% - They reveal who they work for.
1% - They trick you into thinking they work for another civ.
If the enemy spy moved before you caught them, they count as traveling.
If the Civ they belong to is friendly or neutral they are sent on home. (They respawn back in their capital)
If the spy belongs to an annoyed or Hostile civ, they disappear on the road. (They lose the spy)
If the spy didnt move, they are counted as caught in action.
You can then decide to Release them, or Detain them.
If Released you gain 5% of your current espionage points to that civ to show you have info on their spy network. (they also get spy back)
If Detained you gain nothing but they lose 5% their points towards you to show they lost a valuable spy.
If the spy is caught in the act of sabotage, revolt, poison or one of the proper spy actions, there should be real demands made, But only if you know who sent them. (Otherwise they just killed)
Demand they pay you gold, or give you one of their resources for 20 turns or something.
Other actions could be using it to set up diplomacy, you gain +1-2 points with that civ.
Or could have an option for you to gain, or make them lose a good amount of espionage points.
If the spy tricked you (1% chance) and you make demands of wrong civ, it should cause a diplomatic penalty towards you, -2 or such.