If the correct Empires & Puzzles account is not the one on your device, it means you are not using the right one.
Please make sure you’re connecting to the right Game Center account to access the correct gme account.
To properly access your account, please:
1) Login using the e-mail address originally used to sync your account
2) If it’s an old email, contact Apple Support to recover your account’s information.
Small Giant Games cannot access your Game Center account information. If you need help recovering your AppleID (Game Center) you would need to contact Apple directly.