I finished a rank in the Future War Cult. Having done so, I wanted to grab my reward. When I went to the post master, I had both the Faction reward and the public event reward available. Anyway, I chose the faction reward. It gave me a similar reward to the public event. In other words, I didn't get any faction rep for grabbing the reward or any faction items. All I received was glimmer and an Ascendant material.