Does the automatic dispatch hold pre-bookings at a higher priority than ASAP bookings when assigning them?

No, not automatically. You would need to use the priority feature and manually set a higher priority on the pre-bookings entered, to guarantee that they are prioritized over any ASAP bookings entered later. This can be done in the dispatch console under “Extras - Priority” (5 being the highest and 1 being the lowest priority.)

Additional settings can be found in the Admin Panel under the “Assignment” tab here: https://admin.taxicaller.net/admin/settings/dispatch.php