Issue with Joomla Cache and Hikashop cart

-- url of the page with the problem -- : www.mephit.cz
-- HikaShop version -- : 2.4.0
-- Joomla version -- : 2.5.28
-- PHP version -- : 5.3.29
-- Browser(s) name and version -- : Chrome but probably any

Hi,

I am trying to use Joomla caching as in the latest version that I run you have following improvement:

We now clean the Joomla cache when the cart is modified in order to avoid issues with it. Thanks to that, you should now be able to use the Joomla cache with HikaShop without needing specific caching rules

My setting is Joomla Cache / Conservative caching with System - Cache plugin enabled (Use Browser Caching = YES). I am also using JCH Optimize Pro but it doesn"t seem to have an effect on the behavior I am going to describe (i.e. behavior is same when that plugin is turned off):

1) Open new tab in your browser then navigate to page www.mephit.cz
2) Add any item to cart --> notice that it was correctly added to cart.
3) Close the tab with the website (but do not close the browser)
4) Open new tab in your broser and type in www.mephit.cz
5) Notice that cart is empty.
6) Add another item to cart --> notice that after the update cart now contains items added in step 2 and 6.

I would expect either:

i) Cart to not be empty in step 5 with behavior described in step 6) in place

or

ii) Cart to be empty in step 5) and cart containing only item added in step 6) displayed in cart at the end of step 6)

Thanks,

Karol

I only have JCH optimize + Joomla cache enabled, I removed every other optimization that I had (in htaccess) but still have this problem. What additional info would you need from me to investigate this problem?