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.
Best Answer
No, the caster won't take any damage.
The number of hit points you regain from damage absorption depends on the damage you took, but it is otherwise disconnected from the damage. The regenerated HP are, therefore, not "negative damage" that would be reflected as "reversed negative damage" (i.e. regular damage) onto the caster of Necrotic Touch. However, since the target didn't take any damage, the caster won't heal either.
End result: the caster's hit points remain unaffected, while the target regains hit points equal to half the damage roll.
Regardless of the above, both spells use the term "regain". Looking at the definition and using common sense, it's obvious that "regain" can't refer to stealing something from you (in the case of your example, hit points). Since D&D 5e makes heavy use of regular English language (instead of tons of game terms, even though there are some of those in 5e), it's clear that the spell is not meant to deal damage to the caster, even if the spell or absorption would be worded in a way that would render the first section of this answer useless.
Definition of "regain":