You Do Need power plug adapter while traveling from Tahiti to Saint Helena.

Here is Why You Need An Adapter

The outlet and plug type used in Saint Helena is G and in Tahiti are C and E. This is how they look like.

Tahiti

In Tahiti, outlets of type C and E are in use.

Type C

Type E

Saint Helena

In Saint Helena, outlets of type G are in use.

Type G