You Do Need power plug adapter while traveling from Fiji to Turks and Caicos Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Turks and Caicos Islands are A and B and in Fiji is I. This is how they look like.

Fiji

In Fiji, outlets of type I are in use.

Type I

Turks and Caicos Islands

In Turks and Caicos Islands, outlets of type A and B are in use.

Type A

Type B