How do I implement selective refresh with a customizer setting?

Create a function to output the selectively refreshed template code

(I wrapped the HTML within <div class="cta-wrap"> to make it easier to target this particular block of markup.)

function wpse247234_cta_block() {
    if ( ( get_theme_mod( 'intro_page' ) ) != '' ) {
        $intro_id       = get_theme_mod( 'intro_page' );
        $intro_header   = get_the_title( $intro_id );
        $intro_excerpt  = get_the_excerpt( $intro_id );
        $intro_link     = get_the_permalink( $intro_id );
        $intro_linktext = get_post_meta( $intro_id, 'emm_cta_text', true );

        echo '<div class="cta-wrap">';
            echo '<h1>' . esc_html( $intro_header ) . '</h1>' . '<p>' . esc_html( $intro_excerpt ) . '</p>';

            if ( ! get_post_meta( $intro_id, 'emm_cta_text', true ) ) {
                echo '<p><a class="cta" href="' . esc_url( $intro_link ) . '">Learn More</a></p>';
            } else {
                echo '<p><a class="cta" href="' . esc_url( $intro_link ) . '">' . esc_html( $intro_linktext ) . '</a></p>';
            }
        echo '</div>';
    }
}

Update your template with a call to the newly created function above:

wpse247234_cta_block();

Set up the Customizer

function wpse247234_customize_register( $wp_customize ) {

    $wp_customize->add_section( 'intro', array (
            'title'    => __( 'intro', 'text-domain' ),
            'priority' => 999,
    ) );

    $wp_customize->add_setting( 'intro_page' , array(
            'sanitize_callback' => 'absint',
            'transport' => 'postMessage'
    ) );

    $wp_customize->add_control( 'intro_page', array(
            'label'    => __( 'Page to use for intro section', 'text-domain' ), 
            'section'  => 'intro',
            'settings' => 'intro_page',
            'type'     => 'dropdown-pages',
            'priority' => 1
    ) );

    $wp_customize->selective_refresh->add_partial( 'intro_page', array(
        'selector'            => '.cta-wrap',
        'container_inclusive' => true,
        'render_callback'     => 'wpse247234_cta_block',
        'fallback_refresh'    => false, // Prevents refresh loop when document does not contain .cta-wrap selector. This should be fixed in WP 4.7.
    ) );
}
add_action( 'customize_register', 'wpse247234_customize_register' );

Styling the item as it’s being refreshed

While the partial is refreshing, the affected element will have the class customize-partial-refreshing added to it. You can style it like so:

.cta-wrap.customize-partial-refreshing {
    // styles...
}

Helpful links

• Selective Refresh in the Customizer
• Theme Options – The Customizer API
• Taking a look at how Twenty Sixteen v1.3 handles selective refresh was helpful in getting this example to up and running.