After Morpheus is captured, Trinity, Neo, Cypher and the rest all fall down through the gap they were trying to use to escape the building and land on what seems to be some sort of basement, finally escaping all together through the sewers. The next we know is that there's been some kind of "accident" and Cypher is conveniently separated from the rest, and closer to an exit, but it's not clear how they separated and why the rest took a different path. The accident itself doesn't look to me tremendous enough to have them separated.
Cypher was captured by the police after tripping over in the smoke. While Neo, Trinity and the others are making their getaway, he was placed into a police van and then conveniently the police van had an accident, releasing Cypher near a payphone.
[Cypher watches her pry open the grate, when a gas can bounces near him.]
TRINITY: Come on!
Cypher seems to trip as the cloud envelops him. Trinity watches Cypher disappear into the smoke, then follow the others down the wet-black hole.]
The Matrix: Screenplay
EXT. STREET - DAY
[Cypher is standing at a public phone. Across the street is the burning paddy wagon that appears to have collided with an oncoming car.]
CYPHER: There was an accident. A goddamn car accident. All of a sudden. Boom. Jesus, someone up there still likes me.
TANK (V.O.): I got you.
CYPHER: Just get me outta here.
Obviously we know that the accident was no accident, but that's another story.