No.
Next is also a fixed point. The point at which you activate the idea of next. In this case the ability that says "next" is the exact, fixed time the effect is active.
Seriously, the definition states exactly that.
You are trying to argue that a word doesn't always mean what it means and your proof is that the card effect doesn't fit your theory and the definition of the word.
The problem isn't the definition of the word next, or the official ruling on how the card works.
First and next will work the same way in the example for this question. They have to, because the word next does have a meaning, and that meaning fixes the point from which Next is active, and that point is the moment the word is invoked.
In the case of this card game it works the moment the effect that uses the word next is activated.
How else could it be interpreted without ignoring the definition of the word next, and the way it is used throughout the card game.
Next is never used to refer to an ambiguous occurance in the future, it always means the first time after now, now being the moment you invoke "next."
The only way to be consistent with the ruling we have and similar effects that use the "first time each turn" wording is to have them work the same way.
We know "next" isn't consumed by damage that is redirected without requiring the effect that next is attached to.
To resolve how "first" will work we have two options:
1. Ignore the definition of the word next, and how it is consistently used every other time in the game and say that while "First" and "Next" are both not consumed, next can mean the one after the next, while first cannot mean the one after first.
-or-
2. We take the option that doesn't violate the definition of the words, and makes a nice consistent rule and say that damage that is redirected no longer "would have dealt" damage to the original target, therefore first and next don't have to violate their meanings and the whole system works beautifully.
#2 also has teh added benefit of not allowing a single instance of damage to count as damaging one target, but almost damage a bunch of others. Which just seems bizarre to me.
Lastly, yes Next and First have different meanings. The exact nature of which I have made clear multiple times.
First you have to designate the time at which it starts tracking, it can be in the past, in the future, it has to be designated.
Next self-designates that time because it tracks from "now." Now being he moment the word next is invoked.
That is the difference. That difference is irrelevant to this question.
Seriously, you can imagine that next has some wierd true meaning that none of us quite grasp, or you can accept that the definition of the word is accurate and use it the way it is intended to be used.
There is no ambiguity in this usage of next. None. In the example Next and first will work the exact same way.