Doesn't look like they work any differently than the ones I've worked on and the one they sent me to see if I could figure out why it was coming unlocked going around corners. When you say immediate, it actually can't be until there is enough rotation of the tire to line up
He isn't saying it doesn't engage, he is saying the same that I did. Depending on how the teeth in the locking clutches are lined up, the rotation of the tire will be from zero, (immediate) to the distance it has in degrees that the teeth take up. If it had 1 tooth every degree or 360 teeth, it would have to turn a maximum of 1 degree before they engaged. There aren't 360 teeth. If you count the number of teeth, divide that into 360, the number you get will be the maximum number of degrees that is has to rotate before it can lock.
This would be easier if you owned the first iteration of the cable shifter. They didn't put a spring loaded section in it so you had to hold the shifter lever with some pressure on it and then drive with the tires turned until enough side to side differentiation happened for the clutches to line up. You can also see in the pictures the small disengagement springs between the clutches. That is what pushes them apart to unlock them when there is no pressure on them after you hit the unlock part of the switch.