"but could it be that we have TS already?"

No, not at all. The normal wind at Barbados at this time of year is out of the east at about 15mph (think "Trade Winds"). At 9pm the wind at Barbados was out of the east at 32mph (at 8pm they reported a gust to 49mph). The island is currently experiencing the northern edge of the CDO. Because the normal wind flow is being enhanced by the TD to the tune of about 17mph does not mean that the winds near the center of the system are at TS strength - at least not yet. Same thing at St Lucia - normal wind is ENE at 16mph, but currently NE at 29mph. Grenada, where the normal tradewind flow is blocked by the TD circulation, has NNE winds at 7mph - and Grenada is just a little farther away from the TD center than Barbados is. (I guess thats why they call them the Windward Islands

). This is a case where data on the edge of the system has to be weighed with other known meteorological and climatological factors.
ED