Science? The show that neatly splits a man into functional good and evil copies without them apparently losing any mass? heh
Actually, there could be science involved. We know that genes can be switched on or off and we know that our genes affect our behaviour.
If a transporter is a kill and copy machine then popping out two copies instead of one fits with the fictional science.
If the person is instead phased and some sort of quantum linked information is sent but the system adds in replicated matter to make up for any information that leaks away, a malfunction could lead to two copies with a much higher degree of replicated matter than normal I.e. 50%.
The notion of focal points is silly but it was also used in the reboot with Kirk randomly stumbling across Spock in a cave...