Контактная форма показывает подтверждение на новой странице, а не в div (ajax)

Я пытаюсь заставить эту контактную форму работать: https://bootstrapious.com/p/how-to-build-a-working-bootstrap-contact-form но текст подтверждения открывается на новом сайте вместо div «сообщения».

контакт.php

    <form id = "contact-form" method = "post" action = "contactaction.php" role = "form" data-toggle = "validator">
        <div class = "messages"></div>

    <script src = "https://code.jquery.com/jquery-3.3.1.slim.min.js"></script>
    <script src = "https://cdnjs.cloudflare.com/ajax/libs/popper.js/1.14.7/umd/popper.min.js"></script>
    <script src = "https://stackpath.bootstrapcdn.com/bootstrap/4.3.1/js/bootstrap.min.js"></script>
    <script src = "https://cdnjs.cloudflare.com/ajax/libs/1000hz-bootstrap-validator/0.11.9/validator.min.js"></script>
    <script src = "contact.js"></script>

контакт.js

$(function () {

    // init the validator


    $('#contact-form').validator();


    // when the form is submitted
    $('#contact-form').on('submit', function (e) {

        // if the validator does not prevent form submit
        if (!e.isDefaultPrevented()) {
            var url = "contact.php";

            // POST values in the background the the script URL
            $.ajax({
                type: "POST",
                url: url,
                data: $(this).serialize(),
                success: function (data)
                {
                    // data = JSON object that contact.php returns

                    // we recieve the type of the message: success x danger and apply it to the 
                    var messageAlert = 'alert-' + data.type;
                    var messageText = data.message;

                    // let's compose Bootstrap alert box HTML
                    var alertBox = '<div class = "alert ' + messageAlert + ' alert-dismissable"><button type = "button" class = "close" data-dismiss = "alert" aria-hidden = "true">&times;</button>' + messageText + '</div>';

                    // If we have messageAlert and messageText
                    if (messageAlert && messageText) {
                        // inject the alert to .messages div in our form
                        $('#contact-form').find('.messages').html(alertBox);
                        // empty the form
                        $('#contact-form')[0].reset();
                    }
                }
            });
            return false;
        }
    })
});