We haven't seen every little nook and cranny of the Hub. It's possible that Gwen and Ianto and Tosh came down via the lift with the coffee, and at the same time Jack was pelting up a flight of stairs and still managed to exit through the Tourist Office without being seen.

And yes, he wasn't fully recovered at that point but I'm guessing that the knowledge of the Doctor's presence and the desperation to reach him in time could give him a hell of an adrenaline boost.