We updated the file ~2 days ago and the feature we are working on seemingly does not work - web links never open in the app, always end up at the browser.
I set up new test site, added the file there and linked it up with the app. Tapping the link opens in the app.
So my conclusion is that Apple's CDN is not updated. But how I can verify that?
The system will check approximately once a week for an updated AASA.
You can read more here:
https://developer.apple.com/documentation/xcode/supporting-associated-domains
If you trigger a sysdiagnose, in the swcutil_show.txt file you can look for your domain and find information about when the "last check" was, and when the next check will be.
If you are iterating at a fast pace, you can use developer mode, and directly pull the AASA from your web server.
To trigger a download you still need to delete the app and reinstall via Xcode (TF and App Store do not work for developer mode.)