MSNBC confirmed this story was not true.
Lets apply some (sorely lacking on your part) common sense to your tsunami theory. The earthquake you reference is over three hundred miles to the north of the island of La Tortue. This also places it north of the Bahamas, Cuba (NE) and Haiti/Santo Domingo. WERE a tsunami generated, it would have been detected in the Bahamas, Cuba and the main portions of Santo Domingo and Haiti and caused similar effects to what you are claiming for La Tortue. Nothing was idenified in any other direction from the quake site either. Furthermore the island of La Tortue has a maximum elevation of over 300 feet. A 5.4 quake would not generate a 300+ foot tsunami wave. You don't just lose a island. Furthermore, the earthquake is too far away to have lowered the island below sealevel, not without creating a heck of a BIGGER seismic signature than a 300+ mile away quake. Finally, it appears you are grossly unaware of the intensity of a tropical storm rain event - I am having been in the carribean during hurricane season.
Weekly world news does better tinfoil than this because they do better research first. You could learn something from that.