أَدَّبْتُهُ تَأْدِيبًا
Translation: I disciplined him—an act of disciplining.
أَدَّبْتُ: past verb; -tu is the subject.
هُ: direct-object pronoun.
تَأْدِيبًا: cognate verbal noun of أَدَّبَ, parsed as an absolute object in this reconstruction.
In the first source wording taʾdīban states the reason; in the al-Zajjāj reconstruction the verb and its verbal noun share a root.