When curse takes effect

[Clipper]

If you wait until after the combat, then you are correct that they must draw their spoils before you can curse them. The period between actually winning a combat (after giving reasonable time) and the end of receiving the spoils and cleaning up the cards used in the combat does not allow you to play any cards except those that specifically interrupt parts of the cleanup. Thus, you really should wait until after the final Treasure is drawn before playing your Curse.

And as I see thedag already beat me to that, the original Curse is probably Curse! Temporary Amnesia. This makes the user forget their Classes, but it doesn't stop them losing their Class. You could have cursed them before the combat ended if you wanted. Even though they count as having no Class while they are cursed, they would still need to discard the Class card they have if they get hit by a new Curse that tells them to do so.