If your staying onsite then you can take a bus to the Magic Kingdom once you get off, you can walk to the Contemporary which will only take 5 minutes.
If your staying offsite and plan on visiting the Magic Kingdom once your meal is done then park at the TTC and take the Monorail to the Contemporary, because the self parking lot is not to be used as a parking lot for the Magic Kingdom. Once your meal is done you can go right back to the Magic Kingdom for a while and later back to the TTC to pick up your car.
If you are not planning on visiting the Magic Kingdom once your meal is done, then feel free to park in the self parking lot. Once you arrive the security guard will ask for some ID and then check that your name is on the ADR list for Chef Mickey's. Once that is done you will get a 3 hour parking pass and can go threw.