Wikipedia seems to disagree:

The Persians army employed volleys of arrows, slingshots, and javelins against the Greeks in Gaugalema[21] and Thermopylae.[22][23] Ancient Greeks and Romans used arrow volleys.[24][20][19] The goddess Artemis was called "‘of the showering arrows".[25][26]

In medieval Europe, after the initial volley, archers would fire single shots at individual enemies.[27] Examples include the Battle of Hastings in 1066,[28] Battle of Crécy in 1346[19] and the Battle of Agincourt in 1415.[29]

I'd imagine it's possible that a volley meant that they started drawing at the same time rather than drawing and waiting.