For someone to use your adobe account, they would have to log into ADE with the email address and password that is registered with Adobe. I don't think that information is stored on your Kobo.
Now, with Vox, changing your Kobo account password via the website somehow does not automatically trigger a request for a new password on the Vox. This could be true for buying books through WiFi on the Touch. I was told that if you contact customer care they can do something about this.
While waiting for more information, I would change the password and take out your credit card information.
User Guide Link:
http://www.kobobooks.com/touch_user_guides