AJAX dropdown lists dependent & dynamic

Question

I have tried the example I found on Dynamic select list in the form API (dependent dropdown list)? but I did not get it to work properly. The first list populates, but I can not fill the second one with values that are different depending on the first select.

function formtutorial_form(&$form_state) {
  // Connection settings here!!! Then two queries below.
  $stmt = $conn->prepare("SELECT productID, ProductName, oil_ID FROM tb_Products");

  if ($stmt->execute()) {
    $stmt->setFetchMode(PDO::FETCH_OBJ);
    $productlist = array();
    foreach ($stmt as $row) {
      $productlist[$row->productID] = $row->ProductName;
    }
  }

  $productIDselected = $form_state['values']['Products'];
  $stmt7 = $conn->prepare("SELECT oil_ID, OilName FROM tb_Oils WHERE oil_ID = $productIDselected ");
  if ($stmt7->execute()) {
    $stmt7->setFetchMode(PDO::FETCH_OBJ);
    $oillists = array();
    foreach ($stmt7 as $row) {
      $oillists[$row->oil_ID] = $row->OilName;
    }
  }

  $form['Products'] = array(
    '#type'=>'select',
    '#title' => t('Products'),
    '#options' => $productlist,
    '#multiple' => FALSE,
    '#attributes'=> array('size' => 0), 
    '#ajax' => array(
      'callback' => '_ajaxfunction',
      'wrapper' => 'divaroundseconddropdown'
    ),
  );

  $form['Oils'] = array(
    '#type' => 'select',
    '#title' => t('Oils'),
    '#options' => $oillists,
    '#multiple' => false,
    '#prefix' => '<div id="divaroundseconddropdown">',
    '#suffix' => '</div>',
    '#productlist' => array(
      'visible' =>array(
        'input[name="productname"]' => array(
          'value' => $productlist
        ),
      ),
    ),
  );

function _ajaxfunction($form, $form_state) {
  return $form['Oils'];
}