From a phone technicians perspective the answer why it shakes is this:
There is a metal shield that sits over the camera with two screws in diagonal corners. this also acts as a EMI shield however there is an issue with the grounding of your phone and causes the camera to shake due to an interference. When this shield is on it, it causes an electrical current to touch the metal camera housing due to inproper grounding. The best method is to completely disassemble and find the culprit that isn’t grounding your phone properly.
Otherwise removing this shield and securing with some thick tape so the camera doesnt move around is the best economical/DIY option. Keep in mind two screws will have to be removed which very slightly aid reception signals.
Attaching a magnet (especially inside) could severely affect the device and cause a myriad of issues such as poor reception, wifi, bluetooth, lcd warping etc