It largely depends on the techniques used during your surgery. Some techniques rely upon scarring to cause movement of the tip after surgery. This causes contraction. If that scar tissue contracts above the tip, it may lead to increased rotation. This process likely continues for months to years. As always, discuss your concerns with your surgeon as he/she knows the techniques they used.
The aesthetic rhinoplasty manuevers that you mentioned on your post can improve tip rotation. however, for a significant down turned or ptotic tip addressing the size, strength, and position of the lower lateral cartilage will allow for improved rotation. I would speak to your plastic surgeon about the results.