It does take time for the corner of the eye to settle down following a canthopexy. There are many different techniques for performing this procedure and this will also effect the degree of swelling. In general most of the swelling should be subsided by 6 - 8 weeks.
If you only had a canthopexy, then generally you will see the lift to the outer corner of your lower eyelids immediately. However, swelling can mask the improvement to a certain degree early on. Some massage can be done if it is lifted too high, but the timing would be between you and your surgeon. There are slight variances to the technique, so discussing with your surgeon would give you the most accurate healing time-frame.
You should see an immediate result after a canthopexy procedure. However swelling and tightness can persist for several weeks to even months after surgery. Most surgeons, including myself, attempt to slightly "overcorrect" the deformity when performing a canthopexy. This allows amble flexibility so that when the eyelid settles, it appearance doesn't sag further. I tell all of my oculoplastic patients: "The lower eyelid will only settle in one direction: down." Patience is key after this procedure.
Thank you for your question. On average I advice my patients that the angles of the eyelids will look and feel tight for about 3 to 5 weeks. It also depends on the surgical technique used and on the suture material.
Best advice is to ask your plastic surgeon and he will be able to give you a more precise estimate on the ground of his experience with his technique in other patients.
All the best