When I tried to perform a fromTo tween, the onComplete:myFunction was executed as soon as the tween became active and not after the tween had run its course, as I had expected.
According to the existing documentation reference which was not immediately obvious to me, if you're going to do things like add references to onComplete, then you need to associate all such references with the to portion of the Tween declaration - not the from part.
WRONG:
TweenMax.fromTo(dispObj, tween_duration,
{ alpha:fromAlpha,
ease:tween_func,
delay:tween_delay,
onComplete:tweenCompleted,
onCompleteParams:[nexttweenID] },
{ alpha:toAlpha });
CORRECT:
TweenMax.fromTo(dispObj, tween_duration,
{ alpha:fromAlpha },
{ alpha:toAlpha,
ease:tween_func,
delay:tween_delay,
onComplete:tweenCompleted, onCompleteParams:[nexttweenID] });