Add post through code, visibility on front end

Hi everyone,

I am writing a plugin and in the plugin I want to create a post in a custom post type with wp_insert_post and update_field(Advanced Custom Fields).
The post gets added and shows in admin but not on the frontend.
It only works when manually updating the post in admin.
I allready tried adding visibility.

This is my code:

$reservering = array(
      'post_title'    => ''.time().'',
      'post_content'    => 'Reservering',
      'post_status'   => 'publish',
      'post_type'   => 'reserveringen',
      'post_author'    => 1
    );

    // Insert the post into the database
    $post_id = wp_insert_post( $reservering );
    update_post_meta( $post_id, '_visibility', 'visible' );

    $sloep = willekeurigBeschikbareBootOpLocatie($_POST['boekingsdatum'],$_POST['dagdeel'],$_POST['locaties']);

    update_field('dag', $_POST['boekingsdatum'], $post_id);
    update_field('dagdeel', $_POST['dagdeel'], $post_id);
    update_field('dagdeel_sloep', $sloep, $post_id);
    update_field('geslacht', $_POST['manvrouw'], $post_id);
    update_field('voornaam', $_POST['voornaam'], $post_id);
    update_field('achternaam', $_POST['achternaam'], $post_id);
    update_field('postcode', $_POST['postcode'], $post_id);
    update_field('plaats', $_POST['plaats'], $post_id);
    update_field('telefoon', $_POST['telefoon'], $post_id);

I tried searching the internet, but all suggestions always point to visibility.

I hope you guys have any idea what to do.

Thanks,
Rik