How long does it take for the "puffy" look to permanently go away resulting in a flat areola after implants + areola reduction?

The puffiness can take many months to a year if it's just due to swelling/duct block.  If it's due to a permanent suture, then the suture may need to come out.  You need to see your PS.

Good questions- the puffiness may indeed be temporary. Be patient- in many lift & augmentation patients the healing for final scar & appearance may take a year. Keep checking with your PS. If there is a suture that is causing the puffiness it often will relax/dissolve resulting in flattening. Good luck.

It is hard to tell but the puffiness might be due to a permanent suture that was placed around the edges of the areola. If so this will prevent the areola from flattening until it is cut. Check with your surgeon.

The circular incision around the areola not uncommonly causes prolonged swelling. The swelling seems not to reach the edge of the areola, however. I wonder, therefore,  if the cause is not a Gortex suture that some surgeons use to control areolar size. I think that the areolars are large enough and the scars noticeable enough that a revision may do you well. I would suggest considering conversion to a vertical lift. Although the vertical scar will be added, the procedure will provide better control of areolar size, and with less tension on the closure, the scar should heal better.Discuss with your surgeon. All the best.