The Greek text simply reads that Quirinius “was governing” Syria (he did not hold the official title).
Quirinius (Cyrenius) was actually “Augustus Legate of Syria” (had control of the military and controlled foreign affairs) while Quintilius Varus was “governor” of Syria. In 6 AD Quirinius (759) will receive the official title “governor”.
Tacitus, Histories 5.9
“On Herod’s death [in 4 BC], one Simon, without waiting for the approbation of the Emperor, usurped the title of king. He was punished by Quintilius Varus then governor of Syria”.