Specifically, you are supposed to kill these cultists in order:
Unfortunately, you have to run around the temple quite a lot to find them. The respawn times of the other cultists is pretty fast so you might have to kill a lot of them before you get to your targets. In addition, you might have to fight against other people for kill rights because the Temple is quite popular.
Hints: Sometimes it is better to wait for a respawn of a cultist than to run to another location. This is especially true for the Exarchs.
Important: You can get this mission as low as level 25 so you will have some difficulties to kill the higher level cultists if you are solo. If you are in a team then watch out for messages in the chat window! If other members in your team are too high you won't get rewards.
The mission updates and you will receive a reward after you've killed each group of cultists.