I did some more testing.
What I found out is that also Facebook login and presumably all other social networks will generate a new user if the first user changed his email address in the profile page in wp admin area.
So it's required to disable users from changing e-mail after auto registration, otherwise the existing user will not be recognised on the next login and a new user will be created. The same seems to be the case with the bio/description field value.
I don't use the Theme my login plugin, but there may be a setting in the plugin to prevent users from editing email and bio. Otherwise those fields can be hidden by means of jquery and stop people from seeing them and thereby changing them.
When logging in with Twitter (including bouncer module) however, when the same e-mail address is entered, there's an error notice that this e-mail address is already in use by another account. How will it ever be possible then (with or without bouncer) to link logins through Twitter to an existing account, like it is done with FB,LI,G+ etc.?
By not requiring users to enter e-mail manually on registration. I haven't tested to require e-mail and I don't see a need for it anyway. The registration works as it should without doing it. So I would advice you to disable the requirement for e-mail, delete the users again and try from the beginning and to prevent users from changing e-mail address or Bio description (About me). Name change works fine as far as I can tell. If this doesn't work for you, try to uninstall all other plugins you are using one by one to make sure one of them is not the cause.
As for the bouncer I can't tell, since I am not using it.