Are Vengeful Ancestors’ damage-dealing reactions enough to sustain the Barbarian’s rage?


To sustain their rage at the end of their turn, a Barbarian must have attacked a hostile creature since their last turn or must have taken damage since then. [PHB, pg. 48]

In the level 14 feature of the Primal Path of the Ancestral Guardian, "Vengeful Ancestors," the spirits called by the Barbarian’s rage may do force damage to a hostile creature. Mechanically, the Barbarian is using their reaction to cause this damage. [XGtE, pg. 10]

Is the fact that the Barbarian is using their reaction to cause damage to a hostile creature enough to sustain their rage? Or is this insufficient because the damage is not being caused directly by the Barbarian?