This comes form the book "Black Rednecks And White Liberals" by Thomas Sowell. Pattern in this context refers to patterns of behavior of southerners who inherited them from people from the British Isles who lived in borderlands between England and Scotland. Those people were not reached by English culture and therefore were very violent and engaged in gang fights and very reprehensible behavior, which as a result was embedded in southern culture and because of slavery (which happened mostly in the south) passed onto the culture of black Americans.
Also, when the author is saying that it was Southern whites who first had these patterns of behavior he means first before black people whose behavior they influenced and altered by coexisting for a long time together but the originator of these cultural patterns were settlers from Great Britain.
Although Dr. Bunche presented these as parallels, historically it was of course the Southern whites who first had these patterns, reflecting patterns among their ancestors in Britain.
As the patterns of behavior in question were undesirable is it possible that "reflecting" in this context can mean:
To bring blame or discredit: Hasty preparation of the report will reflect on you.