I'm fairly new to Tweeting manually with Twitter, you don't get any say in the matter that I know of when FAA posts and it doesn't seem I ever got any visitors. I believe it has been said in the Discussions it is more effective to manually Tweet, I don't remember all the technical reasons.
I have been getting more real visitors and not bots since manually Tweeting. There will be others to come along and comment and hopefully support my comment!
Correction, FAA was sending out Facebook images not Tweets for me, just recently started Tweeting, the above reasoning still holds.