Hi,
I think you have some cache activated.
Please check your Joomla configuration (cache) and check that the "cache" system plugin is not activated.
You can also check if your template does not have a cache system include.
When I come for the first time in your website, I see that I "have" already products in my cart but, I was the first time.
More than that, the plugin "hikashop social" is not working (i see the tag in the product page) which it means that cache is activated.
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.