In Jeddah, no. There is a specific transit desk where the buses drop you off. Just ask around. Don't go to arrivals/immigration.

After that, you have to climb up/take a lift up 2 floors. It's just a narrow passage and then just randomly try one of the few doors. You will end up airside, after departure immigration but before departure security.

Only in Medina, you have to get an immigration officer to walk you through arrival immigration and then back through departure immigration as they don't have proper transit facilities.

Will fly though Jeddah in 2 weeks time again, and will report if there has been any changes.