From the FAQ Friday of June 17th 2016:

Barbarian Increased Damage Reduction: The increased damage reduction rage power says it increases the “barbarian’s damage reduction”, but does that refer to the barbarian class feature “damage reduction” or to any damage reduction the barbarian might possess. In particular, the invulnerable rager archetype trades away the barbarian’s damage reduction class feature for a new ability called invulnerability that gives a slightly different form of damage reduction, so would the rage power work with that?

The rage power refers to the class feature damage reduction, meaning that it doesn’t help invulnerable ragers’ invulnerability class feature. The suggestion for the archetype to take that rage power in the suggested rage powers is in error and will be removed in the next errata.

There’s some ongoing conversation about the impact of these changes in the PFS forums. Be sure to update your invulnerable ragers before you next play!