if you are experiencing coolant moving from radiator to bottle by squeezing pipes with engine dead cold the inner ring of the radiator cap neck is not sealing to the radiator cap smaller rubber seal. Check to see if there is corrosion or distortion there on the neck. One picture looks like a small piece is missing there. The coolant should only move to the expansion tank when the system pressure lifts the big spring.
One more thing to notice..
when you place the radiator cap on the neck without turning to close it you should be able to press it down with your hand slightly, This test is to determine your cap actually is making contact with the lower ring.
Also make sure the vacuum hat is also sealing itself and nothing is jammed in it (I have seen some mechanics wrap a wire in it claiming ' iss se presshar nahin banay ga)