I tend to think of acid arrow as creating enough acid to cover the surface of the primary target. When the target is hit, it riles back in anguish and some of that acid gets thrown off of it and splashes in the nearby surrounding area.
With respect to the original question of range, I thought of something that may add to the discussion.
If acid arrow was only intended to affect targets within range 20 of the caster, it would be phrased more like the fighter power Giant's Wake (phb 81).
it allows for a secondary attack, and is phrased:
Secondary Target: Each enemy adjacent to the primary target and within your melee reach.
So, my argument would be, if acid arrow was intended to attack secondary targets within range 20, I think it would be phrased as:
Secondary Target: each creature adjacent to the primary target and within range 20 from the caster.