Ok, seems like this issue appears only if your display fps is higher than _physics_process frequency. You can try it out by lowering _physics_process frequency in the Project Settings -> Physics -> Common -> Physics FPS. For example you can set this value to a 10 for example and see how movement become jittery.
This page tells:
Godot 3.1 does some improvements to this, from allowing kinematic bodies to be animated in the regular _process loop
So I think that the affirmation like "Kinematic body movement should be handled in _physics_process only" relates to versions below 3.1