Once you have drilled and cut all of the holes to roughly the size they need to be peal off the 3M painters tape and the template as one piece. You will now see the rough edges of your cuts.
Take the actual pieces you want to mount and keep cutting and test fitting them until they all fit.
From there you can make the box look as good as you want to. Sometimes the holes and rough edges will never show or they dont need alot of work. Its a good idea to take a file to knock off the rough edges and to get the corners perfect.
After a little bit of work and a good template you should have something that looks close to a laser cut piece of plastic that perfectly holds your buttons, switches and connectors.