To have your Facebook updates also shared with your Twitter followers you need to link your Facebook page to your Twitter account. It is very easy to link these two accounts:
1. Sign in to you Twitter account and also Facebook account.
2. Go to this page on Facebook: http://www.facebook.com/twitter
3. Choose a page and click ‘Link to Twitter‘.
4. Now authorize Facebook to use your Twitter account. Click ‘Authorize app’.
5. Now Your Facebook Page is linked to your Twitter account.
You can also edit the settings what you would like to share on your Twitter feed. You can choose to share: Photos, Status Updates, Events, Links, Notes, and then click ‘Save Changes‘.