Apptoto can notify booked appointments if the event is moved or deleted from your calendar.
When enabled, Apptoto will treat any change in the time or calendar of the event as a new appointment. Deleting the appointment would notify the client that the event is inactive. This option is controlled in the Settings>Advanced & Privacy section of your account, as shown below:
If your workflow is to allow the appointment to be booked and then move the appointment to another calendar and do not want the client to be notified, disabling this option would not interfere with that process.