"However, sexual promiscuity arrived in North Africa via the Western conquests"
A definition of "promiscuity" will depend on the local laws governing relationships. In cultures where property is inherited by the first born son then it is considered important to keep women isolated from other men.
The Ottoman Empire ruled over much of North Africa for at least 500 years until about 1919. Polygamy, concubines, and large harems were standard practices that the West would have considered promiscuous behaviour.