Q: I want there to be a way to track my affiliates for any sale that has been made on their part after their visitors have subscribed to my newsletter but only when they have purchased my product.
A: There is nothing tricky about getting that set up. You would just have the landing page for the affiliates be your newsletter opt-in page.
Then you would put your tracking code on the confirmation page after somebody has purchased your product.
Set a cookie/return days period that works for both you and your affiliates, so that they get credit for purchases by their referrals.
Those referrals will be cookied when they go through the affiliate link to hit your newsletter opt-in page.
I don’t know anything about your newsletter, but I’d suggest that you encourage purchases of your product in the welcome e-mail for your list.
Maybe even provide a coupon code for a discount to increase the likelihood that affiliates will get sales.