That whole scene it interlinked with when the keymaker is telling them what to do. It is a bit muddled but if you watch it as many times as say myself and Jedi have, it's pretty simple. Jedi basically got it right.
tshirt> See how the light kinda engrossed Neo like an enzyme eating something... if Morpheus was there, it would have still only taken in Neo. It's to do with recognition of his code, think DNA replication.
Okay, I buy that, that makes the most sense. I think it comes down to muddled directing, not muddled writing. The suspense to the audience is them opening the second backdoor too early, but at the same time they need to get through quickly since they are on the clock. Also throw in Smith stopping them from opening the door too quickly (Smith saves Neo's life by distracting him) and you have a nice bit of suspense. To me it felt like that suspense was totally over when they made it out of the backdoor, when in fact it was still there since they had to get through the door of light. Link counts down during this scene, and then cheers when they make it through the backdoor in time, another signal that they were safe and made it in time. That's where I got confused.
Thanks everyone!