The city developed from a Canaanite Phoenician colony into the capital of a Punic empire which dominated large parts of the Southwest Mediterranean during the first millennium BC. (wiki)

Punic inscriptions were found here (pre-Roman)

"A democratic regime was established in the later 5th century BC (...). This came to a brutal end in 406 BC, when it was besieged and sacked by the Carthaginians. It struggled to regain its former glory, and succeeded briefly under Timoleon, who crushed the Carthaginians in 340 BC and brought in new colonists." (AB Ev) "The city was disputed between the Romans and the Carthaginians during the First Punic War. The Romans laid siege to the city in 262 BC and captured it after defeating a Carthaginian relief force in 261 BC and sold the population into slavery. Although the Carthaginians recaptured the city in 255 BC the final peace settlement gave Punic Sicily and with it Akragas to Rome."
See en.wikipedia.org

Puig des Molins and Sa Caleta are both described in the AB ev as "Phoenician-Punic"

"bears exceptional witness to Phoenician-Punic town planning" (OUV)

Criterion (iii): Tipasa bears exceptional testimony to the Punic and Roman civilizations now disappeared.

"Phoenician/ Carthaginian shrine that ceased functioning in the third century BCE" (Nom File)