You Do Need power plug adapter while traveling from South Korea to British Virgin Islands.

Here is Why You Need An Adapter

The outlet and plug type used in British Virgin Islands are A and B and in South Korea is F. This is how they look like.

South Korea

In South Korea, outlets of type F are in use.

Type F

British Virgin Islands

In British Virgin Islands, outlets of type A and B are in use.

Type A

Type B