As paulm said, the zen_image_submit and zen_image_button functions don't pass the parameters on to the zenCssButton function but they do pass on the sec_class (secondary class) parameter. To get an additional class added to a button, you need to make the call as:
Code:
zen_image_submit(BUTTON_IMAGE_IN_CART, BUTTON_IN_CART_ALT, '', 'my_new_class');
Note also that the zenCssButton function creates a <span></span> structure for calls from zen_image_button, but creates an <input type="submit" /> structure for calls from zen_image_submit.