If someone casts Vampiric Touch on a creature with necrotic absorption, does the caster take damage?

Leaving aside the question of if there’s any way in the manual for anyone to have necrotic absorption in 5e (which as far as I know isn’t the case), and given the text of Vampiric Touch as follows, would attacking a creature that heals from Vampiric Touch do damage to the caster? Vampiric Touch:

Make a melee spell attack against a creature within your reach. On a hit, the target takes 3d6 necrotic damage, and you regain hit points equal to half the amount of necrotic damage dealt. Until the spell ends, you can make the attack again on each of your turns as an action.

It has been brought to my attention that damage absorption is not actually a keyword. The following explanation is sourced from The Rise of Tiamat (aka Tyranny of Dragons) campaign, attached to the dragon masks.

Damage Absorption. […]whenever you are subjected to damage of that type, you take none of that damage and regain a number of hit points equal to half the damage dealt of that type.