There is more that one way to narrow the lapel. Sometimes the jacket can be cut under the lapel inside of the breakline on the chest. This works when the buttonhole is cut.
If the lapel is narrowed on the lapel edge, you want to make sure the grain line of the cloth stays parallel to the lapel edge. It will look chopped up and wrong if you do not. I would question very carefully how your tailor would do it. You don't want the tailor with the lowest price. If he does not understand the outcome he is creating, you lost a jacket. If the jacket is canvassed and has top stitching or pic stitching, it is a lot of work. I did a lot of these in the 80's and would charge 150.00 back then. You don't want to discern that the jacket has been altered when it is finished.