Unholy Might and Wither on hit for spell minions

Hi.

I am planning on buying the forbidden jewels for Unnatural strength. The idea is that all my minions will aplly wither on hit with both attacks and spells and thus boost any source of Chaos damage.

So yes it says "wither on hit" but maybe there are prerequisites for this condition.

So my question is if minions with non-chaos damage spells, fex a flame golem, will inflict wither stacks with unholy might?

Thank you for the confirmation seaman.