To get the tasks from Sunbird, you'll need to use the getItems function. You can either call this on every calendar that you get from the calendarManager via getCalendars. or from the composite calendar, which contains all data of all checked calendars. Note that you'll need to use the filters defined for these calendars. You can look at how either Sunbird's task list or Lightning's task list for an example that gets tasks from the composite calendar.