Clearing the cookies you created won't help you because the user is still signed in with Azure AD. This means that Web-SSO (Single-Sign-On) is running. Regardless of the protocol that you use to authenticate with Azure AD, you still need to properly implement Sign Out - the combined exit! This applies to any web provider you find on the Internet - Google, Facebook, LinkedIn, Twitter, you name it.
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public void SignOut()
{
WsFederationConfiguration fc =
FederatedAuthentication.FederationConfiguration.WsFederationConfiguration;
string request = System.Web.HttpContext.Current.Request.Url.ToString();
string wreply = request.Substring(0, request.Length - 7);
SignOutRequestMessage soMessage =
new SignOutRequestMessage(new Uri(fc.Issuer), wreply);
soMessage.SetParameter("wtrealm", fc.Realm);
FederatedAuthentication.SessionAuthenticationModule.SignOut();
Response.Redirect(soMessage.WriteQueryString());
}
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