Hi,
As far as I can see, they don't use standard HikaShop add to cart buttons.
It should normally be done with such code:
$cartHelper = hikashop_get('helper.cart');
echo $cartHelper->displayButton(JText::_('ADD_TO_CART'), 'add', $this->params, $url, $this->ajax, '', $max, $min);
like in the file "quantity" of the view "product".
That way, it uses the javascript of HikaShop to handle the add to cart.
The form in HikaShop also contains a return URL hidden parameter:
<input type="hidden" name="return_url" value="<?php echo urlencode(base64_encode(urldecode($this->redirect_url)));?>"/>
Which tells the system where to redirect after the add to cart. I don't see that hidden parameter in the add to cart code of that module.