Since your purchase is through iTunes, you will not have to log-in. The sign-in area is for print subscribers only. Your verification is your apple ID and password.
If you are having issues accessing your purchased content in the Fast Company Magazine App you may have to delete the app from the iPad Newsstand (hold down the cover icon for three seconds and tap on the black "X") and re-download it from the Apple App Store. The issues to which you've subscribed should be available for download at that point.
Upon re-installation you may be prompted to "Restore all purchases".
Please note that your subscription begins with the current issue; back issues from March 2012 are available for purchase within the app.