Hi,
Please check that you don't have any kind of cache system activated in your website.
HikaShop, like any other e-commerce system, is not compatible with the Joomla cache (native cache or the system plugin cache).
Some template provides a cache system too and can generate some troubles.
The other solution can be a modification of the URL (or switch between http and https) where the session cookie is not shared. So the cart, stored in the session will be "lost" (not shared).
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.