No Divination makes your HEALS stronger so it works on Khaimera's Invigorate, Rampage doesnt have a self heal so it wouldnt work on him. Divination, Heal & Shielding is for those innate abilities like Zinx heal even abilities that say Heals x over y seconds the x amount is boosted by how much you got built. Divination would give you a starting 5% but you can build items from the support tree to make that percentage go up. Those numbers are actually very weak i did my own theory crafting and studied the numbers and it turns out all the healers scale with Power so just build mage items because the support items give a little bit of power but not to the extent you can build from Mage tree. Though there are some really good Support items like Everbloom that give Damage reduction on heals and shield or Devotion that heals 12% stronger to Allies under 40% health.
Wrap it up Healing and Health regen are separate and different, there are even effects that refer to Base Health Regen Like Cursed scroll gives you 30% Base Health regen per 100 Health you are missing.