How to display an admin notice after updating plugin settings?

After digging in the setting API I found the answer. Method 1 was correct, but the notification should not be done by hooking to admin_notices, rather by the function add_settings_error

add_action ('pre_update_option_my_var', function( $new_value, $old_value) {
    //Do my validation
    $valid = ( 'correct_value' == $new_value );

    if ( !$valid ) {
         //This fixes the issue
         add_settings_error( 'my_var', $error_code, $message );
    }
    return ($valid)? $new_value : $old_value;
});

In order to display them, this also needs to be added at the beginning of the settings page:

<h2>The heading of my settings page</h2>
<?php settings_errors(); ?>