A customer booked an order for 7pm tomorrow. When does my kitchen actually find out?

Twice. Your managers' group gets a ticket the moment it is booked, marked SCHEDULED with the day and the time, so you can plan. Then, at the slot time minus your delivery ETA, the group is told to start, the riders' group gets the dispatch, and the order moves from the Scheduled tab into New. The rider link is only sent at that second message, because it is a single use ticket for a delivery that is about to happen. Nothing needs pressing in between. The Orders & delivery tab in the docs covers scheduled orders.