Hello,
Thank you for the clear report, we were able to reproduce it and it is indeed a bug that was present in 6.5.0.
In a recent version of HikaShop the product page was changed so that it is no longer wrapped in a single form element (this gives more freedom for customization). As a side effect, when the options are displayed as checkboxes, the add to cart was sending the option to the server even when its box was left unchecked, so it got added to the cart. The single dropdown works because it always sends an explicit "No" value, which the server ignores.
The good news is that this is already fixed in the current build of HikaShop. You just need to update: download the latest HikaShop package from your account on our website and install it over your current site (installing over an existing install only refreshes the files, it does not touch your data). After that, do a hard refresh on your frontend and the checkbox options will only be added when they are actually checked.