The governor (ʿāmil) and the case sign are different things.
The governor causes the grammatical status; the case sign makes that status visible.
جَاءَنِي زَيْدٌ — Zayd came to me.
Governor: verb «جَاءَ». Sign: ḍamma.
رَأَيْتُ زَيْدًا — I saw Zayd.
Governor: verb «رَأَيْتُ». Sign: fatḥa.
مَرَرْتُ بِزَيْدٍ — I passed by Zayd.
Governor: preposition «بِـ». Sign: kasra.