Hi,
I think that you're having both buttons but the "add to wishlist" is hover the "add to cart".
Due to the fact that you're using the carousel, I think that the CSS from the JSN template had some missing rules ; because it has not been test in that specific condition/configuration.
You can see in our demo website the different configuration where you can be sure the display is fine :
demo.hikashop.com/index.php/en/hikashop/...display-with-effects
I think it will be easier, otherwise it means that you have to see with JoomlaShine how fix the CSS for that specific setting.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.