It depends. It should not cost any more to change the color if they paint just the outside of the car. But when you open the doors, trunk,etc. You will see the old color.
You can take care of this by painting all visible surfaces, it is much more labor intensive. They can either mask & tape the interior OR they can remove the interior (door panels, rubber moldings, etc. ). Removal is best - that's how it is done on a restoration project. It's labor intensive and can add 50% to 100% to the price.