When we ate there after the park closed, they had 3 Disney busses out there waiting when we were done.
The drivers ask you what resort you need to go to and direct you to a bus.
The drivers communicate with the restaurant on the radio to see how many people are left in the restaurant and if they need transportation. I assume that once it gets close to closing, they start asking guests if they need transportation. We waited about 15 minutes on the bus until one more couple came out and then we were taken to our resort. No one else got off so I assume they were dropping at several resorts.
Now, this was in late 2004, so things may have changed, but that's how it was done then and the comment from the CM would make sense if this were still happening.
If there are no busses you will have to take a cab. When you get to Disney, ask who they recommend for cab service and program the number into your cell phone, just in case.