You Do Need power plug adapter while traveling from Montserrat to South Korea.

Here is Why You Need An Adapter

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

Montserrat

In Montserrat, outlets of type A and B are in use.

Type A

Type B

South Korea

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

Type F