I would not expect the position of your belly button to change significantly following surgery. The position of the belly button actually changes minimally during surgery as it is attached on a rather short stalk. Provided you had a traditional tummy tuck and not an umbilical float procedure, it is most likely that the short belly button to scar length is due to the positioning of the scar. This is something that is best discussed with your plastic surgeon.
I would be really curious to see pictures. usually it is the scar that is too high rather than the naval being too low. would like to see
The distance between the belly button and the scar does not change much after surgery. Further, if an incision was made around your belly button (indicating that you had the traditional type of tummytuck versus the type of tummy tuck where there is no belly button scar and the umbilicus is simply "floated" downward) then I am guessing your scar is a little on the high side. In a traditional tummy tuck the belly button is left attached to a small stalk which anchors it down to the muscle layer and it is very hard to move it very much in any direction. I would be interested in seeing your pictures. Best wishes.
I usually position the umbilicus back at its natural position based on known anatomic landmarks. Google this article: Reconstructing a natural looking umbilicus.
The distance between the belly button and the surgical scar depends on how high the incision was created, provided that the umbilicus was positioned correctly during the surgery. Yes, please provide photos of before and after.
It is not likely that your belly button position with respect to the tummy scar will change in any significant way.
In performing a tummy tuck, I will move the belly button upwards no more than 1/2 ", if appropriate, but rarely if ever move it downward. Things may change as the swelling subsides. Without a picture, one has to wonder if the tummy tuck scar is somewhat high.
We don't usually move the belly button, rather we cut around it and it stays in the same place and then pull the skin above it over it and bring it out a new hole in the belly skin. That being said, heavier patients have longer belly buttons which do allow for a little variation in the final placement. It sounds more like the incision may be a little high but not able to tell you for sure with out a picture.