I think that when Reade got back to the dorm, he didn't go in immediately. Isn't there a phone call between when he was dropped off and when he entered the dorm?
I think that the cabbie may be wrong about when his return trip was, but I don't know the area so have no idea how long it would take. Dukie07 leads me to think he may hvae been there before the police arrived at 12:55--but I'm guessing.
Making a phone call from outside the dorm makes perfect sense. There is NO reception inside that fortress of a building!!