Master Distiller's bonuses apply to Herald of Thunder, but not Tempest Shield

Master Distiller, specifically If Amethyst Flask Charges are consumed, 25% of Physical Damage as Extra Chaos Damage does not apply to Tempest Shield, even though it does apply to the comparable Herald of Thunder.

Setup:
- Some generic chance to poison from passive tree
- Add physical damage to all hits (Circle of Guilt rings)
- Remove non-chaos damage (Replica Alberon's Warpath)

This leaves these skills with 0 damage, unless they gain extra chaos.

When the skills are activated, consuming amethyst flask charges, Herald of Thunder gains extra chaos damage and becomes able to deal damage and poison, but Tempest Shield's hits still deal 0 damage.

I assume Master Distiller's other bonuses (penetration, critical strike chance) would not apply to Tempest Shield either.

Video (youtube)