Grazie per la risposta.

Tuttavia continuo a non capire perché non ricarica la pagina anche se io la includo.

Ho messo tutto il codice all'interno dello stesso file PHP, eliminando le istruzioni:

Codice PHP:
ob_start();
session_start();

ob_end_flush(); 

pagina.php

codice:
if(isset($_POST["submit"]))
{
    $targetDir = "/path/to/upload/dir";
    $targetFile = $targetDir . basename($_FILES["fileToUpload"]["name"]);
    $upload = 1;
    $fileType = pathinfo($targetFile, PATHINFO_EXTENSION);

    /* Check file size */
    if($_FILES["fileToUpload"]["size"] > 500000)
    {
        echo "Sorry, your file is too large.";
        $upload = 0;
    }
    /* Allow certain file formats */
    if($fileType != "data" )
    {
        echo "Sorry, non valid filetype.";
        $upload = 0;

    }
    /* Check if $uploadOk is set to 0 by an error */
    if($upload == 0)
    {
        echo "Sorry, your file was not uploaded.";
    } 
    else
    {
        if (move_uploaded_file($_FILES["fileToUpload"]["tmp_name"], $targetFile))
        {
            echo "The file ". basename( $_FILES["fileToUpload"]["name"]). " has been uploaded.";
        }
        else
        {
            echo "Sorry, there was an error uploading your file.";
        }
    }
}

<form action="pagina.php" method="post" enctype="multipart/form-data">
    <h3>Upload a file:</h3>
    <input type="file" name="fileToUpload" id="fileToUpload">
    <input type="submit" value="Upload" name="submit">
</form>
Ma il comportamento è lo stesso...