This question already has an answer here:
In Xanathar's Guide to Everything, the Path of the Zealot feature Divine Fury has been changed from an aura potentially affecting multiple creatures to an effect triggered when the first creature is hit by a successful attack on each of the Barbarian's turns during a rage.
Divine Fury (XGtE, page 11)
Starting when you choose this path at 3rd level, you can channel divine fury into your weapon strikes. While you're raging, the first creature you hit on each of your turns with a weapon attack takes extra damage equal to 1d6 + half your barbarian level. The extra damage is necrotic or radiant; you choose the type of damage when you gain this feature.
The Player's Handbook notes on page 196 that:
If the attack involves other damage dice, such as from the rogue's Sneak Attack feature, you roll those dice twice as well.
If the attack that triggers Divine Fury is a critical hit, is a Zealot Barbarian allowed to roll 2d6 instead of 1d6? I feel that this question is sufficiently distinct from How does extra damage work for critical hits? because (a) part of the uncertainty is the result of the ability previously being an aura, and (b) it seems like a secondary effect that isn't an intrinsic part of the attack (the first attack succeeding is merely the condition that triggers it), like a Paladin's Divine Smite or a Rogue's Sneak Attack.