How to react to Isar's collection changes on Flutter?

Question

I am using Isar to save some local data for my Flutter app. The data get saved from the app itself and from a background process (using android_alarm_manager_plus plugin).

In the background process I have something like:

@pragma('vm:entry-point') // Mandatory if the App is obfuscated or using Flutter 3.1+
Future<void> callbackDispatcher(int key) async {
  debugPrint('started WM');
  final dir = await getApplicationDocumentsDirectory();
  Isar? isar = Isar.getInstance(Isar.defaultName) ?? await Isar.open([TaskCollectionSchema], directory: dir.path);
  IsarCollection<TaskCollection> tasks = isar.taskCollections;
  TaskCollection? taskCollection = tasks.getSync(key);

  .....

  if (nextSchedule != null) {
    debugPrint('Updating task schedule time: $nextSchedule');
    task.scheduleTimestamp = nextSchedule.millisecondsSinceEpoch;
    isar.writeTxnSync(() {
      tasks.putSync(TaskCollection.fromTask(task));
    });
  }
  
  .....
}

Somewhere else in the app I have:

  @override
  Future<void> init() async {
    final dir = await getApplicationDocumentsDirectory();
    _isar = await Isar.open([TaskCollectionSchema], directory: dir.path);
    _tasks = _isar.taskCollections;

    Stream<void> taskChanged = _tasks.watchLazy(fireImmediately: true);
    taskChanged.listen(() {
      debugPrint('A Task has changed');
      _refreshSink();
    } as void Function(void event)?);
  }

  void _refreshSink() {
    if (_controller!.isClosed) {
      _controller = StreamController<List<Task>>();
    }
    _controller!.sink.add(getTasks());
  }

Everything works as expected apart from the fact that the watchLazy on the collection is not "listening" when the collection get changed by the background process. How can I trigger the listener from the background activity?