There's a reason that 'overkill' and 'extermination' are two separate medals you know!
To get an extermination, you don't have to kill every individual player on the other team. That isn't how you get it. You can kill the same person 4 times in a row for the overkill and get it.
How do you get the extermination? The ENTIRE enemy team must be dead at the SAME time while you have an active overkill or greater. That means if any of them respawned before you got your overkill, if a single person on the other team is alive, you don't get it.