A Zealot Barbarian gets the feature Rage beyond Death at Level 14 which reads 
>Beginning at 14th level, the divine power that fuels your rage allows you to shrug off fatal blows. While you’re raging, having 0 hit points doesn’t knock you unconscious. You still must make death saving throws, and you suffer the normal effects of taking damage while at 0 hit points. However, if you would die due to failing death saving throws, you don’t die until your rage ends, and you die then only if you still have 0 hit points.

My question is, if a Zealot Barbarian is already a 0 hit points and gets hit by a Disintegrate Spell, does it turn him to dust? Since the Disintegrate spell reads
>A creature targeted by this spell must make a Dexterity saving throw. On a failed save, the target takes 10d6+40 force damage. **If this damage reduces the target to 0 hit points**, it is disintegrated.

Since the Barbarian is already a 0 hit points his hit points aren't being reduced to 0 hit points. Does that mean the Spell won't disintegrate the Barbarian or is my reading of the Spell incorrect?