Interview at Disneyland fine dining restaurants
I worked for the Mouse for many years but please take what I am going to say with a grain of salt as it has been 20 years since I left. Since you are asking this I'm assuming you are not applying to the Professional staff which is handled differently.
The way Disney hiring process works;
A) You Apply
B) You get called into a primary interview. Here you watch a movie or get a lecture with a group of other applicants about what it means to be a Cast Member. From there you go to your interview. At this point you may take a written test. Pretty basic stuff like name the Mother sauces, What's in sauce X, units of measurement etc. Your score along with your past references/experpience will determine the position you qualify for. You will then be offered a job for a specific position. Disney has pretty unique brigade designations.
Prep Cooks- Second Floor Culinary
Line Cooks- Advanced Culinary
Prep Chef- Intermediate supervisor
When you leave this interview you will know if you have been hired by the company and what your hourly wage is going to be. The person that hires you will then give you a list of places that have openings. From there you will return another day and go to secondary interviews with the appropriate professional staff member for each restaurant your primary interviewer sends you to. Those Chef's or managers each have their own interview process so no one can help you with what to expect unless you know what restaurant and Chef you will be interviewing with. Don't sweat it if you don't get the first opening. You've already been hired by Disney @ this point so you will keep going on secondary interviews until you get offered a position in a specific kitchen.
FWIW there used to be a cast members section at the DIS forums as well. It might be worth asking over there for more current information. I should also note that I worked @ WDW.
Best of luck. I enjoyed working for Disney and a lot of great chef's have spent some time with the Mouse.