Does the passive you gain from Gromp, as well as the Cinderhulk, proc spell vamp when being attacked?
The Cinderhulk/Bami's Cinder/Sunfire Cape aura does not proc spellvamp or any other on-magic-damage proc except for the healing reduction of morellomonicon. However since it deals magic damage it will benefit from magic penetration.
The Gift of the Toadstool (Gromp buff) works a bit differently. It will apply all magic damage effects (Spellvamp/Liandry's/Rylai's) and it counts as Poison which means a cassiopeia will gain passive stacks and a cooldown reduction of her E against a target that's poisoned with the debuff.
Spell vamp is a magical stat that converts a percentage of the ability damage dealt into health regained. Activated abilities that do not state they "apply on-hit effects" or modify your "next basic attack" will benefit from spell vamp.
Spell vamp works off of activated item effects, Smite, and abilities, regardless of the type of damage done. It is calculated from the damage dealt to the enemy after reductions such as magic resistance, armor or effects like Unbreakable Will.
This makes it clear that spell vamp doesn't actually depend on whether you do physical or magical damage. What matters is that the damage comes from an activated ability that does not do on-hit or next basic attack. Neither Gromp nor Cinderhulk is an activated ability so they will not proc spell vamp.
I can't add a comment but this "This means Lifesteal will be applied fully while Liandry's and Rylai's have reduced effectiveness." is wrong, Liandry's is always applied fully. It has not been reduced for DOT or AOE for quite some time. Otherwise I agree with Jutschge