The fourth name suggests that the boy was adopted, as the suffix -an- usually indicates. A famous example is the emperor Augustus. His name was Octavius, but after his adoption by C. Iulius Caesar his name became C. Iulius Caesar Octavianus. That means that his birth name was Saturius or Saturinus and that the first three names were those of his adoptive father. More common in North Africa was the similar name Saturninus. See Z. Ben Abdallah and L. Ladjimi Sebai, 1983, Index onomastique des inscriptions latines de la Tunisie, p.43 s.v. All these names seem to recall the god Saturnus, who was associated with Baal Hammon, an important Carthaginian god.
Proculus, then, is his biological father. It was not uncommon for Roman men to adopt a son, even when the biological father was still alive. In this case, we do not know whether Proculus still lived or had passed away before or during the short life of the boy.