I thought about how to answer this question, and I can't really think of a way to do it without the answer being pretty simple. So let's hope the mods bear with me.

"Roman-style" reclining at table is not Roman at all, it's Greek, who appear to have developed the triple couches of the τρικλίνιον (more usually τρίκλινος, both words meaning "three couch place;" Lat. triclinium) from similar Near Eastern customs. It appears in central Italy for the first time with the Etruscans, who adopted it from the Greeks, either from mainland contacts or the cities of Magna Graecia--the distinction, for our purposes, is meaningless. The Ptolemids and Seleucids didn't need to adopt reclining at table from the Romans, their people had been doing it for generations, if not centuries, although the Macedonians were comparative newcomers on the Greek mainland to the custom. I don't know what the state of pre-Roman archaeology in Africa is regarding triclinia, but if reclining at table had spread to Africa before becoming a Roman province it was because of the Greeks, not the Romans. There's not really anything else to be said, I'm afraid, the development of the custom from Greece through the Near East is pretty well documented.