How to make get_theme_mod work with AJAX in the customizer preview

Is it possible to make the get_theme_mod work after refresh in the customizer preview pane when it's being called inside a template part by AJAX?

I have a theme that loads the posts on scroll (infinite scroll) and everything works except it doesn't output the updated theme mods in the customizer preview. It only outputs the new theme mods when I hit the save button.

Any idea how to make it update after a refresh as well?

My control settings:

'id'        => 'show_caption',
'type'      => 'select',
'section'   => 'caption',
'transport' => 'refresh',
'default'   => 'top',
'choices'   => array(
  'top'    => __( 'Top', 'my-domain' ),
  'bottom' => __( 'Bottom', 'my-domain' ),
),

InfiniteScroll.php:

class InfiniteScroll {

  private $query;

  public function __construct( WP_Query $query ) {
    $this->query = $query;
  }
  
  public function register() {
    add_action( 'wp_ajax_my_infinite_scroll', array( $this, 'handleAjax' ) );
    add_action( 'wp_ajax_nopriv_my_infinite_scroll', array( $this, 'handleAjax' ) );
    add_action( 'wp_enqueue_scripts', array( $this, 'enqueueScripts' ) );
  }

  public function getPosts() {
    ob_start();

    $this->query->query( $this->getData() );

    if ( $this->query->have_posts() ) {
      while ( $this->query->have_posts() ) {
        $this->query->the_post();
        get_template_part( 'template-parts/post/content' );
      }
    }

    wp_reset_postdata();

    return ob_get_clean();
  }

  public function handleAjax() {
    if ( ! check_ajax_referer( 'infinite-scroll-ajax', 'nonce' ) ) {
      wp_die();
    }

    wp_send_json_success( $this->getPosts() );

    wp_die();
  }
  
  // ...

}

content.php:

echo get_theme_mod( 'show_caption', 'top' );

Ajax request before customize_save: