AnimatedSwitcher with IndexedStack

Try to add key to your IndexedStack and a transitionBuilder method to your AnimatedSwitcher widget like so...

AnimatedSwitcher(
            duration: Duration(milliseconds: 1200),
            transitionBuilder: (child, animation) => SizeTransition(
              sizeFactor: animation,
              child: IndexedStack(
                key: ValueKey<int>(navigationIndex.state),
                index: navigationIndex.state,
                children: _tabs.map((t) => t.widget).toList(),  
              ),
            ),
            child: IndexedStack(
              key: ValueKey<int>(navigationIndex.state), //using StateProvider<int>
              index: navigationIndex.state,
              children: _tabs.map((t) => t.widget).toList(),  
            ),
          ),

There are also cool other transitions like ScaleTransition, SizeTransition, FadeTransition

If you need to use IndexedStack.

You can add custom animation and trigger it on changing tabs, like that:

import 'package:flutter/material.dart';

void main() => runApp(MyApp());

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: MyHomePage(),
    );
  }
}

class MyHomePage extends StatefulWidget {
  @override
  _MyHomePageState createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> with TickerProviderStateMixin {
  final List<Widget> myTabs = [
    Tab(text: 'one'),
    Tab(text: 'two'),
    Tab(text: 'three'),
  ];

  AnimationController _animationController;
  TabController _tabController;
  int _tabIndex = 0;
  Animation animation;

  @override
  void dispose() {
    _tabController.dispose();
    super.dispose();
  }

  @override
  void initState() {
    _tabController = TabController(length: 3, vsync: this);
    _animationController = AnimationController(
      vsync: this,
      value: 1.0,
      duration: Duration(milliseconds: 500),
    );
    _tabController.addListener(_handleTabSelection);
    animation = Tween(begin: 0.0, end: 1.0).animate(_animationController);
    super.initState();
  }

  _handleTabSelection() {
    if (!_tabController.indexIsChanging) {
      setState(() {
        _tabIndex = _tabController.index;
      });
      _animationController.reset();
      _animationController.forward();
    }
  }

  @override
  Widget build(BuildContext context) {
    List<Widget> _tabs = [
      MyAnimation(
        animation: animation,
        child: Text('first tab'),
      ),
      MyAnimation(
        animation: animation,
        child: Column(
          children: List.generate(20, (index) => Text('line: $index')).toList(),
        ),
      ),
      MyAnimation(
        animation: animation,
        child: Text('third tab'),
      ),
    ];

    return Scaffold(
      appBar: AppBar(),
      bottomNavigationBar: TabBar(
        controller: _tabController,
        labelColor: Colors.redAccent,
        isScrollable: true,
        tabs: myTabs,
      ),
      body: IndexedStack(
        children: _tabs,
        index: _tabIndex,
      ),
    );
  }
}

class MyAnimation extends AnimatedWidget {
  MyAnimation({key, animation, this.child})
      : super(
          key: key,
          listenable: animation,
        );

  final Widget child;

  @override
  Widget build(BuildContext context) {
    Animation<double> animation = listenable;
    return Opacity(
      opacity: animation.value,
      child: child,
    );
  }
}

This is a cleaner way to use IndexedStack with animations , I created a FadeIndexedStack widget.

https://gist.github.com/diegoveloper/1cd23e79a31d0c18a67424f0cbdfd7ad

Usage

body: FadeIndexedStack(  
    //this is optional
    //duration: Duration(seconds: 1),
    children: _tabs.map((t) => t.widget).toList(),  
    index: _currentIndex,  
  ),