Repository: flutter
Issue: TabController does not consistently update TabBarViews when same controller is used
Labels: c: regression,framework,f: material design,has reproducible steps,P2,found in release: 2.10,found in release: 2.11,team-design,triaged-design

The effect of using version 2.10.0 is as follows. When only one page is swiped, the status of the two pages can be kept the same. When multiple pages are continuously swiped, the page of page1 cannot follow page2.

https://user-images.githubusercontent.com/7686137/153108503-ed957f7e-2474-476c-b32b-5b3271d1a4c7.mp4


With version 2.8.1, the behavior is normal, and the two pages can be consistent.

https://user-images.githubusercontent.com/7686137/153108890-37db62c2-1aaa-450c-b84d-7611edf4e2d4.mp4
<details>
<summary>code sample</summary>

```dart
import 'package:flutter/cupertino.dart';
import 'package:flutter/material.dart';

void main() {
  runApp(const MyApp());
}

class MyApp extends StatefulWidget {
  const MyApp({Key? key}) : super(key: key);

  @override
  State<MyApp> createState() => _MyAppState();
}

class _MyAppState extends State<MyApp> with SingleTickerProviderStateMixin {
  late TabController _tabController;

  @override
  void initState() {
    super.initState();
    _tabController = TabController(length: 3, vsync: this);
  }

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: Page1(tabController: _tabController),
    );
  }
}

class Page1 extends StatelessWidget {
  const Page1({
    Key? key,
    required this.tabController,
  }) : super(key: key);

  final TabController tabController;

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: const Text('Page1'),
        actions: [
          CupertinoButton(
            child: const Text(
              'To Page2',
              style: TextStyle(
                color: Colors.white,
              ),
            ),
            onPressed: () {
              Navigator.of(context).push(
                CupertinoPageRoute(
                  builder: (_) => Page2(tabController: tabController),
                ),
              );
            },
          )
        ],
      ),
      body: Column(
        children: [
          SizedBox(
            height: 50,
            child: TabBar(
              controller: tabController,
              tabs: const [
                Text('yellow'),
                Text('blue'),
                Text('red'),
              ],
              labelColor: Colors.red,
              unselectedLabelColor: Colors.black,
            ),
          ),
          Expanded(
            child: TabBarView(
              controller: tabController,
              children: [
                Container(
                  color: Colors.yellow,
                ),
                Container(
                  color: Colors.blue,
                ),
                Container(
                  color: Colors.red,
                ),
              ],
            ),
          ),
        ],
      ),
    );
  }
}

class Page2 extends StatelessWidget {
  const Page2({
    Key? key,
    required this.tabController,
  }) : super(key: key);

  final TabController tabController;

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: const Text('Page2'),
      ),
      body: Column(
        children: [
          SizedBox(
            height: 50,
            child: TabBar(
              controller: tabController,
              tabs: const [
                Text('yellow'),
                Text('blue'),
                Text('red'),
              ],
              labelColor: Colors.red,
              unselectedLabelColor: Colors.black,
            ),
          ),
          Expanded(
            child: TabBarView(
              controller: tabController,
              children: [
                Container(
                  color: Colors.yellow,
                ),
                Container(
                  color: Colors.blue,
                ),
                Container(
                  color: Colors.red,
                ),
              ],
            ),
          ),
        ],
      ),
    );
  }
}
```
</details>

<details>
<summary>flutter doctor -v</summary>

```
[✓] Flutter (Channel stable, 2.10.0, on macOS 11.6 20G165 darwin-x64, locale
    zh-Hans-CN)
    • Flutter version 2.10.0 at /Users/haijun/flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision 5f105a6ca7 (7 days ago), 2022-02-01 14:15:42 -0800
    • Engine revision 776efd2034
    • Dart version 2.16.0
    • DevTools version 2.9.2
    • Pub download mirror https://pub.flutter-io.cn
    • Flutter download mirror https://storage.flutter-io.cn

[✓] Android toolchain - develop for Android devices (Android SDK version 31.0.0)
    • Android SDK at /Users/haijun/Library/Android/sdk
    • Platform android-32, build-tools 31.0.0
    • Java binary at: /Applications/Android
      Studio.app/Contents/jre/Contents/Home/bin/java
    • Java version OpenJDK Runtime Environment (build 11.0.10+0-b96-7281165)
    • All Android licenses accepted.

[✓] Xcode - develop for iOS and macOS (Xcode 13.1)
    • Xcode at /Applications/Xcode.app/Contents/Developer
    • CocoaPods version 1.11.2

[✓] Chrome - develop for the web
    • Chrome at /Applications/Google Chrome.app/Contents/MacOS/Google Chrome

[✓] Android Studio (version 2020.3)
    • Android Studio at /Applications/Android Studio.app/Contents
    • Flutter plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/9212-flutter
    • Dart plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/6351-dart
    • Java version OpenJDK Runtime Environment (build 11.0.10+0-b96-7281165)

[✓] VS Code (version 1.64.1)
    • VS Code at /Applications/Visual Studio Code.app/Contents
    • Flutter extension version 3.34.0

[✓] Connected device (2 available)
    • 2109119BC (mobile) • bcdbd14b • android-arm64  • Android 11 (API 30)
    • Chrome (web)       • chrome   • web-javascript • Google Chrome
      98.0.4758.80

[!] HTTP Host Availability
    ✗ HTTP host https://maven.google.com/ is not reachable. Reason: An error
      occurred while checking the HTTP host: Operation timed out
```
</details>