Actually, I solved it. For the position property in range selector animation I used:
var boxWidth = thisLayer.sourceRectAtTime(time).width;
[-boxWidth,0]
and no need to link the Anchor Point to the position property of the characters in Range Selector Animator.
The only thing I found there is a small offset position of characters like A, V.. vs. B, L, P …. but that’s another story. Anyway, thank you!