After rewatching the scene (again), it basically boiled down to running out of time.
The first level kick is already happening, they hadn't got Fischer in the room by the locked gate. Cobb forces Ariadne to tell the team the secret entrance (the air vent ducts) but in doing so (because Cobb was in earshot of Ariadne ) he obviously heard about the secret entrance too.
So telling just the team wasn't an option, maybe Cobb could have ran over into the bushes and pulled his ear piece out or something but because they were panicking and rushing Cobb overruled Ariadne, forcing her to just tell everyone about the secret entrance.
Also another reason why Cobb asked and deemed it necessary is because of Cobb's character, which is even highlighted by his team mate Arthur in the film:
Arthur: So now you've noticed how much time Cobb spends doing things he says never to do.
Cobb is so arrogant or reckless with his subconscious projections (Mal) that he thought it would be ok if he over heard the secret entrance.