How does paypal clear the cart in the shop?

-- url of the page with the problem -- : dadshotsauce.com
-- HikaShop version -- : 2.2.2
-- Joomla version -- : 3.2
-- PHP version -- : 5.3

We have been running some tests before launching our new shop.
in one of the tests a user did the following:

Purchased one product
Checked out with Paypal
Paid with Paypal
Closed the browser

Shortly after the user went back to the site and he found the product still in the cart.
I asked them to repeat this and other purchases they made because they didn't sound too sure about the exact procedure implemented but at the same time it occurred to me that I am not so sure how Paypal and Hikashop handle the clearing of the cart after purchase/payment with paypal.

So while I wait for the tests to be performed again and see the results, I wanted to ask here if anyone could explain to me how Hikashop and Paypal handle the clearing of the cart after payment and if there are any situations where after purchasing and paying for something it is possible to find that product still in the cart.

Is it necessary for the user to click on "return to website" button in the paypal confirmation page?
If the browser window is closed at that point, does that impede paypal from communicating with hikashop that the product has been purchased?

Thank you.

Thank you so much.