It's really messed up. I've had countless debates with ZONE and FLEET and TEAM over it. Some think you need to capture zones and have people there to reduce their points.
I've been in games where we've controlled 4 out of 5 zones and their influence never budged. I personally think all you need to do is control 1 zone and defend it while killing people trying to take your zone. I've seen feds do it countless times.... just balling up into 1, ignoring the rest, and winning.
In my experience, you have to capture the points by waiting at it about 20secs to remove the point from the other side, then over a minute to actually make it start giving you points. It doesn't really tell you when a point is captured though so people usually fly off when it looks like its done.