Add to cart form AJAX not working when loading a product display via AJAX
The reason why it redirects after adding to cart is because the add to cart form doesn't use ajax by default. Wich causes it to redirect the user when submitted. 
If you want it to use ajax you'll have to alter the submit button via a 
HOOK_form_FORM_ID_alter.

For more info on the form ajax functionality
FAPI ajax

However by doing so you'll alter all the add to cart button forms on your entire website to use ajax. 

So a better solution might be to create a custom add to cart form just for the product_quick_buy view-mode and display that instead of the standard form. This form can then use ajax to call it's submit handler. 

Also I think your ajax link implementation for the hook_menu doesn't follow the coding standards. 

function tweaks_menu() {
  $item['product/get/ajax/%'] = array(
    // -- your code -- 
    'delivery callback' =&gt; 'ajax_deliver', // Tells drupal we'll be returning an ajax renderable array
  );
  return $items;
}

function tweaks_get_product_ajax($nid) {
  $node = node_load($nid, NULL, false);
  $node_view = node_view($node, 'product_quick_buy');
  $html = drupal_render($node_view);
  // Instead of printing we're generating an ajax renderable array and return that
  $commands[] = ajax_command_html('YOUR_JQUERY_SELECTOR_HERE', $html); 
  return array('#type' =&gt; 'ajax', '#commands' =&gt; $commands); 
}


More info about ajax links Tutorial on ajax links