Slingbadger and Archaeoman refer to Vegetius, who I think recommends release after one spin, instead of three (which rather suggest that the three-spin release was normal, as indeed most ancient sources seem to suggest). He also does mention training to sling. Note this is not for "slingers", but for legionaries. The speech of Hadrian at Lambaesis also mentions slings, including slinging on horseback.
http://www.livius.org/la-ld/lambaesis/lambaesis_inscr.html(the horseback thing isn't there but it's been referred to in this forum earlier).
So:
-drilling by legionaries in the use of the sling is very likely: legionaries drilled, and the Lambaesis inscription shows that they did sling in the C2nd AD.
-"standardized length" and "volley fire" and "all in synch" are perhaps less likely, especially since the Lambaesis thing seems to be about individual prowess (which the Roman army had considerable time for: this is shown e.g. by Caesar's account of the Gallic Wars, or Josephus on Roman cavalry. The point made I think by Jacques Harmand is his book on Caesar's legionaries). But that's arguable.
Anyways, it's Vegetius (unsurprisingly), to which add the Lambaesis inscription recording a speech of Hadrian. Good to know not just what (we think) we know but how we know it.