Yes, both should be plugged in to supply power to the cpu. The reason it's working at the moment (and it won't for long) is that the cpu's power is all being drawn through the single connector. Not a good situation. If you stress the system, you can melt down the connector.
If you notice the 8 pin connector came with a cap over four of the pins so that you only have to plug in the four pin connector and if you plan on overclocking then you would plug it the other four pin connector.
Though this motherboard provides 8-pin ATX 12V power connector,
it can still work if you adopt a traditional 4-pin ATX 12V power
supply. To use the 4-pin ATX power supply, please plug your
power supply along with Pin 1 and Pin 5.