Set the old_parent_id and old_position values on model load. This way, when save is called on the loaded models (which have not changed parent nor position), it doesn't think it needs to update the positioning because of the logic in setupReordering (since old_parent_id === parent_id && old_position === position).
Added a check to testCreate (now testCreateSetsPosition) that once an entity is saved to the database, its old_position === position.
Added a test (testCreateSetsRealDepth) that verifies that the real_depth is set on entity creation (it was not the case).