The $render function does the following:

controller.$render = function () {
                        var viewValue = controller.$viewValue;
                         if (viewValue) {
                            var date = moment(viewValue);
                            if (angular.isDefined(date) && date != null && moment.isMoment(date)) {
                                datetimepicker.data('DateTimePicker').date(date);
                            }
                        } else {
                            datetimepicker.data('DateTimePicker').date(setCalendarPickerStartDate());
                            datetimepicker.data('DateTimePicker').date();
                        }
                        return controller.$viewValue;
                    };

So, I believe that datetimepicker.data('DateTimePicker').date(date); causes the onblur event to fire

as we have

scope.$watch('ngModel', function () {
                        validate();
                        datetimepicker.on('dp.change', updateModel).on('blur', onblur);
                    });

I'll try to add a new variable that will tell me what kind of change it was.

Looking closer I think the code that causes the problem is this:

 scope.$watch('ngModel', function () {
                        validate();
                        datetimepicker.on('dp.change', updateModel).on('blur', onblur);
                    });

I've been tracing and I can see that angular sets the control dirty in that watch check.