As Steve Bird implied in his comment, firing at a very large target that isn't moving doesn't require pinpoint accuracy. Nonetheless, some degree of accuracy would undoubtedly have been desirable.
W. T. S. Tarver, in The Traction Trebuchet: A Reconstruction of an Early Medieval Siege Engine (this link downloads a pdf) makes several observations "based on five years of experience with this kind of machine".
Among them are:
- One discovery was that
By shooting as fast as possible (a bit over four shots per minute) the operator and the crew fall into a rhythm which makes the shots more powerful and consistent.
- Later in the trials,
an even more effective method of shooting was discovered.
Very simply, the crew counts to three, giving a light tug on each of "one"
and "two," and hauling through on "three." This slightly slows the rate
of shooting but coordinates the pull of the crew to a remarkable extent.
- Tarver also realised that
consistently sized ammunition is crucial for
accurate shooting because the mass of the projectile is an integral part
of the dynamic system which propels it.
On this last point, Tarver gives some examples of cluster patterns achieved by a team of 16 pullers:
with a 41-inch sling and a 5-inch hook set at 40 degrees discharged six 4.7-kg balls in one minute and ten seconds to distances of 81, 79, 76, 77, 76, and 76 m
a different crew of fifteen pullers using the same hook and sling settings shot six 4.7-kg balls to distances of 100, 90, 105, 100, 105, and 93 m. The second 100-m ball landed on the first, destroying both.
Travers also states that
….In 1989, I could usually strike a round target 10 m in diameter a distance of 90 m away on the second shot given consistent ammunition, and accuracy improved in 1991. Medieval artillerists took great care to control the weight of their shot, having each projectile chiseled to a near-perfect sphere.
Although "identical ammunition is best", Travers believes a skilled operator should be able to "compensate for variations of up to plus or minus 10 percent in mass".
In building and operating the traction trebuchet, Tarver made use of medieval illustrations and, most importantly, "the military manual of Mardi b. 'Ali b. Mardi al-Tarsisi, written around A.D. 1187", but he also points out that (being made primarily of wood) none have survived so it is impossible to be sure exactly how they were constructed.
This illumination from the Bible de Maciejowski shows how, sometimes, the operator didn't release until he was off the ground. Attrib: The Morgan Library & Museum [Public domain], via Wikimedia Commons
A final point worth making is that traction trebuchets had a faster rate of fire than the more accurate counterweight ones so there was some compensation there.