[redirect] yii2 redirect in controller action does not work?

Don't use exit(0); That's bad practice at the best of times. Use Yii::$app->end();

So your code would look like

$this->redirect(['index'], 302);
Yii::$app->end();

That said though the actual problem was stopping POST requests, this is the wrong solution to that problem (although it does work). To stop POST requests you need to use access control.

public function behaviors()
{
    return [
        'access' => [
            'class' => \yii\filters\AccessControl::className(),
            'only' => ['create', 'update'],
            'rules' => [
                // deny all POST requests
                [
                    'allow' => false,
                    'verbs' => ['POST']
                ],
                // allow authenticated users
                [
                    'allow' => true,
                    'roles' => ['@'],
                ],
                // everything else is denied
            ],
        ],
    ];
}