Hi,
Well, first, I only see that issue the first time I add something to the cart on your website. If I then add a second product, it works properly.
And on the first time when it doesn't work properly, I can see a javascript error on the page:
i.imgur.com/aevISns.png
And I don't get that error when it then works fine.
I think the issue happens because all the HTML / javascript of the page is compressed by an optimization extension but it's too aggressive and it renders the javascript code on the invalid:
i.imgur.com/fx4hnFx.png
This leads to the javascript error, which prevents HikaShop from loading properly on the page and thus the add to cart works in degraded mode and has to redirect to the checkout as it can't display the notification box because it hasn't been initialized properly in the first place.
So I would recommend deactivating the HTML/javascript compression on your optimization extension and it should hopefully fix the problem.