The vet appointment is different to the USDA meeting. You have a vet inspection, of which they complete the forms, and then you take the forms to the USDA to inspect and stamp. Once USDA certify the forms, then you've 10 days to ship your cat.
Be sure to arrive at the USDA place as early as possible. In Los Angeles USDA, there was a ticketing system (you arrive, grab a ticket and wait for your number to be called), which was available from 7:30am to 11am. Once you got your ticket then you had to wait. We arrived at 09:45am and waited 6.5 hours to get processed. If you arrive after 11am then you're told to come back the next day.
Be sure to have your vet's phone number to hand as the USDA person inspected our forms, saw a mistake which meant we had to phone the vet to update the signed form to fax to the USDA.