Hi,
This happens because the HTML of the right area is inside the description area which is refreshed when you change the selection of the characteristic.
This can have two causes:
1. In your product description, you have invalid HTML which breaks the page structure.
2. You (or your template developer/designer) customized the product page layout in a wrong way which creates invalid HTML on the product page.
So the problem is not in HikaShop. One simple thing you can do is to edit your show_default view file via the menu Display->Views (I suppose that it's the one that was customized and that you're using on your product pages), and change the text hikashop_product_description_main (2 of them) to something else so that the characteristic refreshing system won't find the description main area and thus won't refresh it.
But I would recommend to contact your developer/designer if you're not the one who did the customization on your product page as it might require a more complex modification.