When the rear air conditioner is on, when I first start the vehilce there is a popping noise in the back, on the passenger side

The rear AC and heater is located in the back. The popping noise is probably a blend door shutting or opening. My Expedition is having a similar issue and I am going to check it out pretty soon.

Yup, temp blend door motor or function door motor. They ar right nest to each other just behind the c pillar. if you remove the rear cupholder there and the flat area below the 3rd window yo will see them both. When first turned on and clicking adjust the temp knob from hot to cold and back a couple of times and listen for any change. Then adjust the floor ceiling selector and listen for any change. whichever one changes its tone or quits clacking is your culprit.