Does iOS Universal Link work with website redirections?

Question

I have completed the setup of iOS Universal Links from official Flutter guide. Including hosting the AASA file in my server's /.well-known/apple-app-site-association:

{
  "applinks": {
    "apps": [],
    "details": [
      {
        "appID": "ABC123.com.test.test",
        "paths": [
          "/test/*"
        ]
      }
    ]
  }
}

So my URL works if I click it from my Notes or Slack app.

Or if I run in my terminal:

xcrun simctl openurl booted https://<domain.com>/test

For example, <domain.com>/test?response_type=token&client_id=abc123...

There are a couple of redirections in my web app when I click a button, at certain point it calls the said URL with /test path. So my problem is it doesn't automatically open the app through that redirection.

Moreover, ONLY in Safari browser, will a banner that says Open in the Test app.

I understand that it doesn't work if I manually input that URL in the browser address bar.

But does Universal Link's nature, work only when clicked or am I missing anything?