Hello @David136,
No sure about the synching but sharing my bits: yes, there are guests who just go ahead and book without intially communicating just by looking at the details and promising previous reviews of the property. However that happens quite rarely, most guests talk before bookimg. Never experienced a delay, I use the App, and also have my email notifications on. I get an instant notification whenever there's an instant booking.
However it is possible that you might be occupied with some other task and might miss the notification or the mail and thus a double booking could happen if you fail to update your calendars on other sites.
Hope that helps 🙂