How do I automatically post or publish my Tumblr posts to my Facebook page? I don't mean the News Feed one, but a Facebook page.
The staff answers your question here:
The simple answer:
Go to this link -- http://apps.facebook.com/tumblr-feed/ to activate it
If the default Tumblr one isn't working you can try a third party.
I've used If This Then That
Find the "recipe" or make your own: if Tumblr then Facebook