Answer
When the automatic SSO login attempt pop-up appears, click Cancel on it rather than waiting for it to fail on its own — canceling that automatic attempt is what reveals the manual account-selection/credential-entry screen underneath, letting the user pick 'use a different account' and enter their credentials directly. Unticking 'Use single sign on' alone doesn't stop IEE from still attempting the automatic login first; canceling that specific pop-up is the extra step needed to actually reach the manual login option.