Even if both crowns are gens, there are multiple versions of Triplock crowns with varying dimensions. So even when replacing 1 gen crown for another (assuming differing versions) could result in an ill-fitting crown.
By the way, there is no relation to the orientation of the coronet on the face of the crown & it proper fitment of either the crown or tube. Orientation of the coronet is mostly luck-of-the-draw (dependent on tube dimension/position, depth of tube in the case, length of stem, thickness/condition of gaskets, etc).