Cloudfront and multiple Country code top-level domains

Question

I did deploy a Next.js application on aws-amplify and everything works fine. Additionally I started to add six custom domains to my application on amplify (mysite.at, mysite.de, mysite.com, mysite.uk, mysite.it and mysite.ch). This works well too.

Now I wanted to use the i18n feature, which nextjs provides.

module.exports = {
  generateEtags: false,
  i18n: {
    locales: ['en-US', 'it-IT', 'de-AT', 'de-DE', 'de-CH', 'en-UK'],
    defaultLocale: 'en-US',
    localeDetection: false,

    domains: [
      {
        domain: 'www.mysite.com',
        defaultLocale: 'en-US',
      },
      {
        domain: 'www.mysite.it',
        defaultLocale: 'it-IT',
      },
      {
        domain: 'www.mysite.ch',
        defaultLocale: 'de-CH',
      },
      {
        domain: 'www.mysite.at',
        defaultLocale: 'de-AT',
      },
      {
        domain: 'www.mysite.de',
        defaultLocale: 'de-DE',
      },
      {
        domain: 'www.mysite.uk',
        defaultLocale: 'en-UK',
      },
    ],
  },
}

It's possible to call www.mysite.com/de-DE and it shows me the page for Germany, ww.mysite.com/it-IT for the italian content and so on.

But when I call www.mysite.at (which should render the content for Austria de-AT) I always get the content from the first call which was made after deployment. In this case I always get the content for Germany.(on every machine I try)

When I empty the cloudfront cache, and call www.mysite.uk I get the content for uk, but when I call www.mysite.de afterwards, I get the uk content again.

When I request with a parameter eg. www.mysite.de/?dsjskdjsaj it does work.

So I think the cloudfront CDN (Lambda@Edge) is the problem in this case. Is it possible to cache the content for each domain? I know there is only one cloudfront distribution for my project, but maybe there is a solution.