Aconius (or Aco) Catullinus was probably a son of the identically-named senator who served as governor of Africa in 317–318.
In 338–339, Catullinus served as vicarius of Africa, and is attested on 24 June 341 as praetorian prefect of Italy.
A law (Codex Theodosianus, 16.10.3) addressed to (and likely suggested by) him, dated 1 November 342 during his term of office, concerns the preservation of pagan temples.
Catullinus had a daughter, Aconia Fabia Paulina, who married the senator Vettius Agorius Praetextatus.
According to the Chronograph of 354, Catullinus bore the informal name (signum) Philomatius, which some authors have emended to Philomathius (meaning love of learning), but Salway suggested instead Philematius, from the Greek φίλημα (kiss).