You'll need to create a pair of products for the shipping products you use in the International Shipping Add-on.

So if you have Domestic and International, you would have 4 products total for that:

DOMESTIC STRIPE
DOMESTIC PP
INTL STRIPE
INTL PP

If you want to offer FREE domestic shipping to USA (or any other country), then you would actually just use a random product ID when setting up the configuration, so your DOMESTIC PRODUCT ID would be:  0000000, and International would be whatever the actual product ID is.

If you set it up like the latter (with free Domestic Shipping), you would only need to create INTL STRIPE and INTL PP products.