SharePoint web application not using the good Trusted Identity Token Issuer

We have a SharePoint 2016 farm and 2 web applications. We have configured SSO through ADFS and created one SPTrustedIdentityTokenIssuer for one web app. Now, we want to have a second SPTrustedIdentityTokenIssuer for the second web app. We made the same configuration, changed the realm, added a new certificate, etc …

The issue is : – When we connect to a site on the second web app, it automatically sends the realm of the first identity token issuer, and we face this issue :

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Now, if we change the default sign-in page on the web app, like this

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We then are able to select between “Windows Authentication” and our second trusted identity token issuer. If we select it, the good realm is sent to ADFS and we can connect to the site.

Any idea about what’s going wrong ?

We could provide any additional information.