By default twitter module try to add a different twitter account to each drupal user so if you try to add a single twitter acount to all drupal user
you need to do this steps:
1- Check all the installation process for a single account work.
2- Go to permission (admin/people/permissions) and check this options:
-Add Twitter accounts
-Use the site global Twitter account
-Assign a Twitter account as the site global account.
3- go to a account and add the twitter account, then will appear a option to do this twitter account global check and save this option.
4- add the global twitter account to each user.