First, 6 magnet vs. 12 on the PAS sensor, I don't think you'll notice much difference in response time. Response should start from the time the first magnet passes the sensor, so 1/6 of a turn vs. 1/12 of a turn.....
Second, the motor should start providing assist as soon as the controller senses the pedals are being turned. Full power doesn't come right away though. It's a "soft start" setup so people aren't startled by the power coming on line. This was one of the big reasons I didn't care for RAD's controller set up and went with a KT system. When I'm crossing a busy street for instance, and I tell it to GO, I want it to GO NOW, not accelerate at a snails pace. When I tell it to go now, I had better be hanging on with both hands....
Finally, not familiar with the '16 RAD product, but no assist power below 6 or 7 mph doesn't sound right to me. That would not last long on my bike for sure. The throttle should be active from a dead stop, no different than the PAS should be active from the time the pedals start to move.