Flutter – understanding multiprovider and streams

I think I couldnt understand the multiproviders in flutter, how it works.

I want to share two version of MyTabs class, you can see them in the following.
The problem in the second version is that the stream is being listened to only when the Third tab is selected but I do not need to do that in the first version of MyTabs class, it automatically listens to the stream without selecting the Third Tab.

import 'dart:async';

class StreamData {
  final StreamController<int> _valueStreamController = StreamController<int>();
  late Stream<int> valueStream;

  int _counter = 0;

  Stream<int> get myStream => _valueStreamController.stream;

  int get streamCount => _counter;

  StreamData() {
    valueStream = _valueStreamController.stream;
    _startTimer();
  }

  void _startTimer() {
    Timer.periodic(Duration(seconds: 1), (timer) {
      _counter++;
      _valueStreamController.add(_counter);
    });
  }

  void dispose() {
    _valueStreamController.close();
  }
}

First Version

class MyTabs extends StatelessWidget {
  MyTabs({Key? key}) : super(key: key);

  @override
  Widget build(BuildContext context) {
    final Stream<int> myStream = StreamData().myStream;

    return DefaultTabController(
      length: 3,
      child: MultiProvider(
        providers: [
          StreamProvider<int>(
            create: (context) => myStream,
            initialData: 0,
          ),
        ],
        child: Scaffold(
          appBar: AppBar(
            title: const Text('Tab Demo'),
            bottom: const TabBar(
              tabs: <Widget>[
                Tab(text: 'First'),
                Tab(text: 'Second'),
                Tab(text: 'Third'),
              ],
            ),
          ),
          body: const TabBarView(
            children: <Widget>[
              FirstScreen(),
              SecondScreen(),
              ThirdScreen(),
            ],
          ),
        ),
      ),
    );
  }
}

Second Version

class MyTabs extends StatelessWidget {
  MyTabs({Key? key}) : super(key: key);

  @override
  Widget build(BuildContext context) {
    return DefaultTabController(
      length: 3,
      child: MultiProvider(
        providers: [
          StreamProvider<int>(
            create: (context) => StreamData().myStream,
            initialData: 0,
          ),
        ],
        child: Scaffold(
          appBar: AppBar(
            title: const Text('Tab Demo'),
            bottom: const TabBar(
              tabs: <Widget>[
                Tab(text: 'First'),
                Tab(text: 'Second'),
                Tab(text: 'Third'),
              ],
            ),
          ),
          body: const TabBarView(
            children: <Widget>[
              FirstScreen(),
              SecondScreen(),
              ThirdScreen(),
            ],
          ),
        ),
      ),
    );
  }
}

I couldnt figure out multiproviders and streams in flutter how they works.