Hi,
Well, checking the situation on your website, it looks much better than before.
Before, When I went to other pages, I could see numbers not correlated at all to what I really had added to my cart.
Now, it's always the correct number.
So turning off the caching on your pages really did help.
I now only see a small glitch as you explain in your last message, whereby sometimes when I click on the add to cart button, the number in the cart module doesn't refresh but if I try another add to cart, or go to another page it is properly updated.
But that only happens on the second and third link you gave, not the first one.
And on the first one, I can see the popup of the add to cart, but I don't see it on the two others after the add to cart.
I think this is linked to the customization you did on the add to cart button of these two other pages.
There, the attribute data-addToCart of the a tag has been changed to data-addtocart. Because of that, the add to cart cannot be done in ajax anymore and it works in degraded mode, redirecting the whole page to the add to cart controller, and then redirecting to the checkout. And to avoid going to the checkout, as you didn't want that, you cheated and added a window.location.reload() on the span around the img tag of the add to cart link so that it stays on the current page.
I would recommend to remove that, and fix the case of the attribute of the add to cart link. That should then work with the ajax mode and the cart module should then refresh properly, like on your first link.