AFAIK they were not granted full independence - from some declassified State Department memos I was looking at, when Eric Williams tried to force the US to withdraw from its bases in Trinidad the British government re-assured the US that if Williams became too extreme in his demands they (the UK) could remove him from power.  Since this was during the Federation (1960, if I remember correctly) I would infer that the Federation was not independent.  Other than that I just have negative proof - that I have never heard of an independence ceremony (which, if it had happened would have been in Trinidad, since the Federal capital was there) and the fact that most of the islands reverted to being British possessions after dissolution.