That's both correct and incorrect. E-V13 did arise in West Asians. However, it specifically arose in West Asians that belonged to E-M78 in the first place. That's the clade E-V13 is a branch of, as the passage just quoted makes clear:<quoted text>
Actually no Europeans who carry EV13 didn't share common ancestors withe North Africans or Ethiopans. If you notice the passage you posted states the EV13 marker is not common among Africans and that EV13 arose in West Asia among West Asians. If anything Europeans who carry the EV13 marker share common ancestors with West Asians since EV13 arose among them.
"it represents about 85% of the European E-M78 chromosomes with a clinal pattern of frequency distribution from the southern Balkan peninsula (19.6%) to western Europe (2.5%)."
Out of curiousity, what lineage did you think that E-V13 branched off of if not E-M78? You also realize that the most basal and rare E-M78* paragroup has been found at its highest frequencies in North Africa, Southern Europe and the Balkans, right?