Hi.
But the issue is not with the add to cart button.
If you choose a variant from the drop down menu and then you decide that you don't want that variant but another one, and you choose another variant from the drop down menu, you will see that your second choice doesn't load.
You might see that the drop down menu change the name, but this is fault since the product page doesn't load. Product name or image, if there is an image for every product, are still from the first choice you have done.
It doesn't matter if you click the add to cart button slow or fast, since the variant product its not loaded. When you click the add to cart button it just add the first one you have selected.
As I have said, I have use the default vm template on that page and the variant works like it supposed to. You can change your variant at any time and the new product will load. Then you click the add to cart button and you are adding the variant you have choose.
Can you check it again please?