Amazon will pay $1 billion to the government as a penalty and set aside $1.5 billion for consumers. The settlement terms have most of the details. [0]
Amazon will do an automatic payout to some people for up to $51. No need to claim anything for that. I'm guessing they'll mail checks or prepaid debit cards or something.
Then Amazon will make a website, within 30 days, and post it on their site (and I'm sure news media will also post it) that will be for manual claims. These claims are also for up to $51 and people will have 180 days to manually claim.
After that, if there's still money, then Amazon will repeatedly do more $51 automatic payments to more people until they're out of money (basically more lax automatic qualification of Prime members from June 23, 2019 to June 23, 2025).
I don't think anyone gets paid a lot more than $51 but it's possible I read it wrong.
It read like more people get $51 but no one gets more than $51.
It wasn't 100% clear to me if some people could maybe get up to $51 twice (ie. automatic claim followed by manual claim) but it read fairly explicitly to me that they couldn't get it more than that.
The bit at the end where they pay out all the extra money doesn't read like it goes to the same people multiple times but instead opens up to an ever expanding pool of people (there are hundreds of millions of prime members).
This wasn't a class action lawsuit, so the process will be a bit more strict. But yes, ultimately there is a pool of money set aside for payments and everyone will get a tiny bit ($51).