This node, “Arcane Absorption”, in the ‘Rip Blood’ skill tree is applying to all on-hit damage no matter the source. So either the text is wrong or the skill is bugged.
Without casting Rip Blood I just achieved this spell damage bonus from ‘chain-sacrificing’ my skeletons on a group of barrels at the end of an arena wave.
I have verified that I do not get any spell damage bonus when I despecialize out of Rip Blood, and that I get it again when I pick it back up. Also I have used another skill ‘Hungering Souls’ with the same result.
I just confirmed it also works with Basic Attacks, so looks like any on-hit like I was guessing.