Public computer login / Authorized Device?

If I use 1password.com on a public computer and check the "public computer" box it gets added to the Authorized Devices list in my profile.

@bergersride: Correct. It has to be authorized in order for you to actually login and do anything there. But this is temporary.

Keep in mind that it is risky to access your account or any sensitive information on a machine someone else controls. This is not recommended, and something which should only be done in an emergency.

I'm not sure if this is supposed to happen, it seems confusing since the public computer was only authorized while I was logged in and shouldn't have a copy of the secret key.

This is important so that a record of every device signed into is reflected in your account. This is the same as signing into your account in a browser without checking "this is a public or shared computer", which will store the Secret Key in the browser's local storage, and then subsequently resetting the browser — or computer — completely: it will not longer have the Secret Key stored locally, but it will still show up in your authorized devices list since 1Password.com has no way of knowing you nuked it. All 1Password.com sees is the login session; everything else is done locally on your machine, so it has no way of knowing the status of the Secret Key being saved locally. I'm sorry for the confusion there, but hopefully that helps clarify. :)