This is a bit of nationalist revisionism. 'Serbia' didn't exist in Roman times. The Slavs who would later make up the former state of Yugoslavia and Bulgaria hadn't migrated into southeastern Europe yet. Geographically too, Serbia was not a particularly distinct part of the Roman Empire. Serbia, as in the modern state, was divided between two or three provinces. Greater Serbia was divided among even more. The more accurate analysis is that even more than eighteen Emperors came from the Eastern European parts of the Roman Empire, what is today former Yugoslavia, Hungary, Romania, and Bulgaria.

And to be clear, the statistic is itself inaccurate. It often identifies people born in other modern southeastern Slavic states as Serbian. But for some reason, it excludes others born in regions that are from territories of modern Slavic states. That the list itself is inconsistent points to some issues. (Edit: I just realized, some of them are Pannonian. Part of that is in Serbia, but it's mostly in Hungary! The Magyars weren't there yet but that territory isn't Slavic even today...)

The reason for this is unexciting: that area was a frontier region between a vast plain of barbarians and a wealthy, populous part of the Empire. It was thus a heavily used recruiting ground and contained something like a third of the Roman army, one of the largest concentrations. During and after the Crisis of the Third Century, military support was important for taking the throne. So commanders in a region with a hugely disproportionate part of the Roman army had a significant advantage. This is also why you had Emperors from, say, Britain, despite the fact Britain was a backwater. It was a border region that required significant garrison, and that garrison could be used to support a march on Rome.

From The Illyrians, The World of Late Antiquity, and Rome and Its Empire, 193-284.