Hi,
You say that the HikaShop cart system should be able to work with the Joomla cache turned on, but it's technically not possible, and it's not because of a problem in HikaShop but because of the way the cache system works.
The goal of a page cache system, like the one in Joomla, is to store a copy of the page that has been processed so that next time the user or someone else accesses the page, the cached version is automatically sent to the user, without processing the whole page again.
Here is an example so that you can understand :
So let's say that you display the product page once. The cache system will store the processed page for later. Then click on the add to cart button on the page. HikaShop will add the product to the cart and then redirects you back to the page you were on. However, as the page you were on was already cached, it won't be processed again. So if you have a cart module on the side of the page displaying the content of the cart, you'll still see that the cart is empty even though you just added a product to it. If you go on another page of the website where the cart module is displayed, you'll see that the product is there.
But then, another user comes in, and when he accesses one of the pages you were one, after you added the product to the cart, it will also see that product in the cart module on these pages sine they were also cached.
To summarize the caching issue: An ecommerce system displays dynamic data and thus, for it to work with a caching system, the cache system needs to be able to take into account that dynamic data and not cache it. Unfortunately, the caching system in Joomla isn't advanced enough to support that and you would have similar caching issues with any Joomla ecommerce solution if you activate the cache.
In fact the caching system is the main cause of problems with cart update issues (based on years of support) and that's why it's the first thing we recommend to check on your website, not because we don't want to fix issues in HikaShop.
And the fact that several people think that they have the same problem because the behavior they see looks the same to them doesn't mean that they have the same problem. For example, if your car isn't starting, it doesn't mean necessarily that the motor is broken. It could well be that there is no gas in the tank or that there is no electricity in the battery.
Now back on topic.
I'll be happy to look at your website in order to understand what is your problem and what we can do to avoid it. Would it be possible to put your website online (even temporarily) so that we can look at the cart ? Also, if you can provide a step by step procedure in order to reproduce the problem, that would be great. That way, we know what to look for.