The operator isn't under the other company, so if they say "we need this data" they can just say no.
Now potentially they could try to trick the operator, but I'm not sure a company could be compelled to do so under US law. While there doesn't appear to be any relevant cases, this would fall under compelled speech (https://en.m.wikipedia.org/wiki/Compelled_speech) and it seems like it would fall on the impermissible side to me.
It seems like they're doing it differently than they did for e.g., China.
Note that the money is simply a matter of a contract (e.g., we will hire your company, which is located in China to operate our cloud region. We'll give you X dollars, and you'll give us Y revenue).
For the Germany region, they're using a mixture of technical controls (e.g., the AWS user has to sign off on accesses in a way that's technically not circumventable (think like a phones unlock screen or something protecting the data on the device) and only allowing AWS employees located in the EU to operate it (presumably the goal being that employees physically located in the EU can't be compelled in the same way as those located in the US).
Amazon licenses the technology to the other company and finances their related infrastructure, in exchange for most of the profit they make from it, or something along those lines, I would guess. It’s a contractual agreement.
Now potentially they could try to trick the operator, but I'm not sure a company could be compelled to do so under US law. While there doesn't appear to be any relevant cases, this would fall under compelled speech (https://en.m.wikipedia.org/wiki/Compelled_speech) and it seems like it would fall on the impermissible side to me.