The Dresden RPG uses the FATE system, so I'll be quoting rules from the FATE SRD
There are two possible concepts to look at: holding an action and readying an action. Holding an action lets you wait until a later point in the turn order to act, usually so that you can wait for an ally to change the battlefield or be in a more advantageous position.
Hold Your Action
A character can opt not to act when his turn comes around. When a character takes a hold action, he has the option of taking his turn any time later in the exchange. He must explicitly take his turn after someone else has finished their turn and before the next person begins. He cannot wait until someone declares what they’re trying to do, then interrupt them by taking his turn.
This doesn't quite get what your player wanted (essentially ambushing the enemy), but it's certainly close.
Readying an action lets you prepare a specific action to perform on a certain trigger. As you say, in D&D 4e a character can use a Standard Action to create an Immediate Reaction to be used later in the round. FATE doesn't exactly have an identical mechanic, but it does have a means to "block" actions.
When the character’s action is preventative – trying to keep something from happening, rather than taking direct action to make something happen – he is performing a block action. He declares what he’s trying to prevent and what skill he’s using to do it. Players may declare a block against any sort of action or actions and may theoretically use any skill, but unless the block is simple and clear, the GM may assess penalties based upon how hard it would be, or how much of a stretch it would be. Players should never be able to “cover all bases” with a single block.
Depending on your player's ultimate goal, he may block the enemy from exiting the building, block the enemy from attacking once he's exited, etc. As the text says, though, the player shouldn't be able to cover all of his bases: be specific in what the character is trying to block.
Another option would be using Stealth to set up an Ambush, which is apparently what the player wanted in the first place.
◉ Ambush [Stealth]
While we can be sure that heroes would never strike an opponent from ambush, they may end up on the receiving end of such nefarious actions! When a strike is made from ambush, the target gets one last Alertness check to see if he notices something at the last moment. On a success, the target(s) can defend normally. If that Alertness roll fails, the attack is made with the target’s first defense roll at Mediocre.