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.

No, the caster won't take any damage.

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.

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":

to take or get possession of something again

Spells and features only do what they say they do, so both the caster and the creature will be healed for the damage "dealt"

Following from this answer, wherein it was discussed that features only do what they have explicitly spelled out, we can see that since neither the absorption feature nor the vampiric touch spell mention a "backflow" affect, the caster would not be damaged by the usage of this spell on a creature with the absorption feature.

Interestingly, since the damage "dealt" is not completely negated (as it would be with immunity to necrotic damage), both the caster and the creature with the feature will heal for half of the necrotic damage "dealt".

If you wish to rule otherwise, you are, of course, welcome to.

Since you are homebrewing the damage absorption, you get to homebrew Everything about it, so really, it's up to you. You can focus on fun / the Rule of Cool. You do not need to rely on the framework in The Rise of Tiamat because you are not in that campaign, and anyway, it doesn't contemplate necrotic damage, which is arguably different in nature.

Clearly the attacker does not realize the target has necrotic absorb.

The house rule should be that necrotic damage absorption divides damage by 2 and turns it negative, and that becomes damage dealt, and backflow can happen. Per the house rule: The damage roll was 12. Due to his absorption, the target heals for half the damage roll, so his healing is 6 and damage is -6.

RAW, via Vampiric Touch, the caster heals for half the damage dealt. Half of -6 is -3, so his healing is -3, meaning damage of 3. Ouch. He won't do that twice.

This quartering of damage keeps it more fun than deadly.