I think maybe this plugin has yet to catch up with Twitter's latest app authentication changes. There is no such thing as a "My Access Token", "On the right hand side of your new application page at Twitter".
Only Consumer Key and Consumer Secret, along with the three URLs.
I would also like to know whether or not I should check to "Use Twitter for login".
Besides this current shortcoming this does however look like an outstanding plugin, and I hope to be using it successfully very soon =)