When you are already registered in a Flarum forum with a standard email-password account and you login with Twitter using the plugin 'flarum-ext-auth-twitter', the existing account with the same email of the twitter account will not be associated. Instead, you will be prompted to register a new account (the form will take your username on Twitter). This behavior works perfectly with the facebook plugin, due to the email permission in the auth request.

I suggest someone Flarum expert which is more comfortable with the codebase to modify the plugin to submit a pull request adding this parameter in the authorization request:
'userProfileURL' => "https://api.twitter.com/1.1/account/verify_credentials.json?include_email=true"
Into the file https://github.com/flarum/flarum-ext-auth-twitter/blob/master/src/TwitterAuthController.php probably here but not sure:
$server = new Twitter([
'identifier' => $this->settings->get('flarum-auth-twitter.api_key'),
'secret' => $this->settings->get('flarum-auth-twitter.api_secret'),
'callback_uri' => $redirectUri
]);
This should fix this issue, combined with the Twitter permission setting enabled.
Reference: https://dev.twitter.com/rest/reference/get/account/verify_credentials