You Do Need power plug adapter while traveling from Réunion to Isle of Man.

Here is Why You Need An Adapter

The outlet and plug type used in Isle of Man are C and G and in Réunion are C and E. This is how they look like.

Réunion

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

Type C

Type E

Isle of Man

In Isle of Man, outlets of type C and G are in use.

Type C

Type G