In case of Google account, your device may be set to auto login and the login details may remain. That is why you are logging in with previous account.
  Please disable auto login feature from your device, and try to login again. 
  
  [Disable Google Auto Login]
  1. Go to device Settings menu.
  2. Account and Backup
  3. Manage Account
  4. Select and delete the device’s logged in account.