Newcomer / Intro Conflict/Warzone help plz (timer ticking)

I picked up a mission to "Destroy Warzone". It's telling me to go to a conflict zone and "end the lives of those miserable Warzone pilots". I've entered multiple conflict zones before, and the two currently present in the mission system. The only ships I've ever seen in those zones are Federal Navy and System Security, both of which are clean to me, and both of which sound like they belong to a faction I don't want to make enemies of. Any advice on how to deal with these things?

EDIT: After a quick forum search it seems people are saying what happens in a conflict zone only affects the zone, nothing outside. Is this the case? I just fly in, pick a side, and kill the opposite? Someone in one of the threads mentioned "unless you have the conflict mission" but didn't elaborate on what difference that made.
 
Yes, it's a conflict zone, so it's basically a civil war between local jurisdictions.
Pick a side in your right panel, and start murd.. I mean, "fight the good cause"
 
they are tougher to take out than your usual pirate.
better shields and most likely (the time to take down) reinforced alloys or military grade composite armour.
 
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