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?