Good Morning,
I'm sure this was working correctly before 1.4.4, but after the update, if I select a Variant, the price on the product detail page is updated, but when I click Add to Cart, the default Product/Characteristic/Price is added, not the selected Variant. Also, after the product is added to the cart, the product page reverts to the default Characteristic setting, but maybe that is normal.
I also have the problem reported in another thread where the Characteristic does not properly get added to the Product name when the Characteristic/Variant is changed on the Product page. The page initially loads with the default Characteristic added to the name but it does not change. This issue was present before the upgrade to 1.4.4 and I suspect it is related to the template I'm using as your demo site does not have this problem.
Regards,
Ed