Your questioning my response got me to check the rulebook and here is the official ruling from the section labeled 'Spawning Enemies':
Official Rulebook p.12 wrote:
If your fear is 7 or more, during this step spawn a clone on the closest vent in addition to any other enemies the event spawns.
In that quote it says "...this step...", it is referring to the Spawn Enemies step. So my first post is incorrect (and shall be edited so future readers don't get the wrong answer!).
Whenever a player whose fear is at 7 or 8 draws an event card, you spawn a clone in the closest vet during the Spawn Enemies phase.