The flat inner damper is what I see on my heads and called the "plastic insert". It is coiled along the inside of the main outer spring just like in the picture, but I still can't make out an inner spring. It looks like a cylinder inside the spring. Could the other spring be inside that cylinder?

If I see the plastic damper is that a sign that they are probably dual spring? or did all 390 heads have them? Thanks for the reply, I feel I'm getting close to solving the mystery.