Cognito Authentication flow session timeout stuck at hosted UI

Hello,

My Cognito user pool has the following configuration:

• Login with Google
• Authentication flow session duration: 3 minutes

Then, I have a login page (using Amplify) hosted at: https://login.example.com/ . The federated login with Google works fine except in the following case:

• I wait at the select Google Account screen for 3 minutes (waiting for the authentication flow session to expire)
• Then, select the Google Account to login.
• Expected result: the login failed, and the browser should redirect to https://login.example.com/
• Observed result: the login failed, and the browser redirected to hosted UI with an error message Something went wrong. Please try again. In the URL, I can see the param redirect_uri is https://login.example.com/

In this case, how can I make Cognito redirects to https://login.example.com/ instead of the hosted UI?

Thank you.