Hello.
You need to configure CRON script at your server to have periodically import.
Please read more about this feature here: https://wpbookingcalendar.com/faq/#sync
Import.
Please check about the configuration of import events from .ics feeds in this FAQ instruction here https://wpbookingcalendar.com/faq/import-ics-feeds/
Please note, the import process is working in that case, when some visitor is open your website page with booking import shortcode. So you can configure CRON at your server, for periodically access this page with booking import shortcode to start import process. Or you can insert the import shortcode before booking form shortcode, so firstly system will start import process and only then show booking form, when someone visit your page.
In case if you are having some issue of not ability to import new events, then check this troubleshooting instruction: https://wpbookingcalendar.com/faq/ics-importing-issue/
You can define CRON at your server for periodically access pages with import .ics feeds shortcodes and start import process during specific time-intervals, then check this: https://wpbookingcalendar.com/faq/cron-script/
Export.
Please check about the configuration of export .ics feeds in this FAQ instruction here https://wpbookingcalendar.com/faq/export-ics-feeds/
Booking Calendar is generate .ics feed with bookings in real time. But how often some service (like airbnb, or booking.com ) access this .ics feed to import the bookings from Booking Calendar into own system, does not depend from Booking Calendar. So in other words, Booking Calendar does not force to generate import process by third party service, when some booking is created. You need to check with support of this service (like airbnb or booking.com), about how often they can access the .ics feed tor making import.
Kind Regards.
