Interrogation Droid reads…

Reaction: After this unit enters pay, discare at random 1 card from your opponent's hand.

My question is this: I played my Interrogation Droid and my opponent had only 1 card in his hand. It was an event and he thought that he had to chance to play his event card BEFORE I discarded it. My thought was that when I played my Interrogation Droid, the card's Reaction went off immediately before he had the chance to play out his event. How does this timing work?

If his event is an interrupt, then he can play it. Otherwise, not.

An interrupt with a trigger appropiate to the situation of course

The active player has the first opportunity to play a reaction after an action. This means that if you take the action of deploying the droid, you have the first reaction in response. Unless your opponent has an interrupt triggered by the deployment of the droid, you may initiate the reaction to its deployment, thus forcing your opponent to discard.