You Do Need power plug adapter while traveling from Turkmenistan to South Africa.

Here is Why You Need An Adapter

The outlet and plug type used in South Africa are C, M and N and in Turkmenistan are C and F. This is how they look like.

Turkmenistan

In Turkmenistan, outlets of type C and F are in use.

Type C

Type F

South Africa

In South Africa, outlets of type C, M and N are in use.

Type C

Type M

Type N