If you want open modal window then you have to use javascript / jquery as shown below
<meta name="viewport" content="width=device-width, initial-scale=1">
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css">
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
<form action="" method="post">
<button type="submit" name="btn">Test</button>
</form>
<?php if (isset($_POST['btn'])) { ?>
<script>
$(function() {
$("#myModal").modal();//if you want you can have a timeout to hide the window after x seconds
});
</script>
<!-- Modal -->
<div class="modal fade" id="myModal" role="dialog">
<div class="modal-dialog">
<!-- Modal content-->
<div class="modal-content">
<div class="modal-header">
<button type="button" class="close" data-dismiss="modal">×</button>
<h4 class="modal-title">Modal Header</h4>
</div>
<div class="modal-body">
<p>Sample modal window</p>
</div>
<div class="modal-footer">
<button type="button" class="btn btn-default" data-dismiss="modal">Close</button>
</div>
</div>
</div>
</div>
<?php } ?>