As far as why Barbossa recognizes Tia Dalma, her deal to bring him back seems to cover that aspect of the story. 

Why the other pirate lords do not recognize her seems to be most easily clarified by a quote from Sao Feng to Barbossa.
>Feng - "The Court has not met in my lifetime."
>
>Barbossa - "Nor mine."
>
>Feng - "And when last it did, my father told me, it ended...badly."

And, according to the [wikia][1]:
>The First Court consisted of the Nine Pirate Lords who bound the sea goddess Calypso in her human form, on the instruction of Davy Jones, who revealed them secrets from the Journal of the Ancient Seas. They sealed Calypso's fate with Nine Pieces of Eight, so that the rule of the seas would belong to men. The Brethren would convene a further three times before Calypso's eventual release.

All this would point to the fact that the Bretheren are a completely different generation of pirates, and thus would not have seen the original binding of Calypso to Tia Dalma's mortal body.

  [1]: http://pirates.wikia.com/wiki/Brethren_Court