But, a defending minion moving in from 1 step sideways will NOT be at rest because once that defending minion uses its triggered ability, it's no longer at rest. It won’t return to being at rest until the whole attack sequence finishes. Also, it's doubly not at rest because it moved!
Units being carried by other units will not be at rest while being moved.
Units being forcefully moved by an effect like or will not be at rest, since they’re being moved.