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It requires a lot more. I can't reveal the specifics of how many points are between each rank, but it's intended for you to have to work at it for a substantial amount of time. Your best bet to move up more quickly is doing the daily quest…
You misunderstood how it works. Killing things does nothing. Only quests will affect which side is in the lead. So, you could turn in your slain warriors to the Aztob npc that wants them and that should push them into control.
The being ahead warriors are those that will have capitalized organization names, like "blah blah warrior of the Aztob" versus the non-varying warriors that will be "blah blah warrior of the aztob". If that doesn't answer the question enough, let me…