My temporary fix was to “Enable the shipping calculator on the cart page” .
My shipping costs are gone on safari and firefox. It works on chrome only.
I found a solution for this here – http://www.sean-barton.co.uk/2013/03/remove-woocommerce-20-reviews-tab/#.UT7p8NGPip1
I edited it for product tab. Code below
add_filter( 'woocommerce_product_tabs', 'sb_woo_remove_description_tab', 98);
function sb_woo_remove_description_tab($tabs) {
unset($tabs['description']);
return $tabs;
}