I think the vaccine used to be administered inside the dome. You never have to get out of your vehicle. Bring ID and be prepared to fill out 3-4 pages of paperwork. You can fill this out as you're being assigned a queue. Shot was administered by SAFD personnel. They write time of shot on your windshield. You are put in final queue to check any allergic reaction. Total time in and out < 30 min. Original website instructions said to go to lot A. Do not do that. Keep driving around back to lot B or C. There are plenty of workers to direct you.
Hope this is helpful.