When the madman narrates his tale, time just drags by, almost coming to a standstill until the instant of the murder. This helps heighten anticipation, suspense and the even the sense of horror. Then as he leaps into action, so the pace of the story line also speeds up until the arrival of the police the next day. Then the whole process of waiting and anticipating and mounting stress repeats itself all over again. Only this time it crescendoes to the revelation of the murder (as the cymbal in an orchestra sounding off) instead of the murder itself.
Poe has been called the master of short stories. He even wrote an essay about it, stressing the importance of working towards a unified effect. His model seems to be inspired from the same "rules" for Greek drama - unity of setting, time and action. As for time, he stressed that the lapse of time in a short story should normally be very short (24 hours or less). Several of his short stories are exceptions, but this is the rule of thumb to go by. Check out the reference below for more information concerning this.