Soni,
Part of the process of air, stool and ground-layering (rooting cuttings as well) is etiolation. In the absence of light, the limb will become more succulent and begins the process of cell conversion to adventious root cells. This is what happened in your pictures. Girdling is used to trap photosynthate generated by the leaves from being sent to the roots to feed the rest of the mother plant. The dam of photosynthate is used to develop roots. That is not to say the layer will not root without a girdle, it will.
I do not like to layer my trees until the end of summer. It is too hot in central Texas for me to comfortably remove a layer too soon. I have (with larger limbs) started etiolating the limbs several weeks before setting an air-layer. I will wrap the area I am going to layer with black electrical tape (sticky side out).
Then remove it before putting on the layering materials.
