Why! Hydra+Summoned Hydra=no proc Firewall encantment

When using Firewall in an enchantment slot and the Hydra with “Summoned Hydra” skill (applies burning) it does not trigger the Firewall Enchantment at all.

Either the Firewall Enchantment tooltip is wrong and should read “burning applied by you and not your conjurations” or it simply is not working.
Where is the error why it doesn’t work?

I’ve noticed this as well. It procs with a self-cast firewall, but does not proc from Hydra at all. These little things really need to be shored up, there are simply too many inconsistencies (seemingly due to bugs) to break out of the meta.