An unchained barbarian does not increase Con so a feat that increases the amount of Con shouldn't work. No mechanics exist on the unchained barbarian to increase Con score so adding Con score improvements to nothing gets you well nothing.
The only way you could even get access to Raging Vitality is if you used the community created Archetype to remove the Paizo rules from the unchained barbarian. Otherwise Raging Vitality is not allowed. This means the second you used the community created archetype you are into your groups houseful territory. As such "each" DM and group will have to decide how this works. In other words the adjustment is the correct way to go. 