We actually just put up version 1.1 because SEF was causing issues with UserMap. If you aren't using SEF, you might be OK. If you are, I would suggest updating.
Were you logged into Joomla when you Connected to Facebook? The way it currently works, after you Connect to Facebook, we make an AJAX call to the component passing the user's Facebook ID. If the user is logged in, we create a mapping from the logged in user to the Facebook ID sent back by Facebook.
Eventually, we want to make it smart enough to ask the user to login/register or require that the user is already logged in/registered before displaying the Connect button, but we wanted to get user feedback to see which way would work better.
Let us know if you can't get the UserMap working. Thanks for helping us!