Apples to oranges. The AA shopping portal does not have Amazon, and the method of tracking is not the same.
I will agree however, that it is flawed. It is flawed in the sense that Jetblue does not control the process; Amazon does.
With AA shopping, Cartera buys the miles from American and contracts with merchants to cooperate with the process (ie providing categorized receipts, broken down totals, etc) for a commission/fee in return for the "referral." Cartera then pays you a small cut of the fees they received from the merchant in the form of miles. If anything goes wrong, you can contact Cartera, and they will research the problem, and credit you if they find that you did everything correctly, and your purchase conforms to the rules. If you didn't read the fine print and/or did not follow the rules, then you will not receive any miles. They pay sooner because they have the ability to claw back your miles if you return the items.
With JetBlue and Amazon, this is all done on Amazon's end. Amazon does not offer the commission as a reward. They simply pay it out to the affiliate which is JetBlue. What JetBlue does with the money is not Amazon's business. So, if something does go wrong, the best thing that can happen is that JetBlue throws some pity miles your way, because JetBlue was not paid. Amazon will not help you as you are not a party to the affiliate program. Amazon does not pay JetBlue until at least a month later because they need to wait for the return window to close. Amazon isn't going to try to claw back money from JetBlue if you return an item.
Either way, you will not receive miles if you do not follow the rules/instructions. If you had an item in your cart before clicking through AA Shopping, I'm willing to bet that your miles will not post there automatically either.
It's too bad that JetBlue doesn't offer any helpful instructions on the partner page to help people who may do things unique to Amazon such as "Save for later."