The reason RJ said the METHOD and the PLACE of his death was important is simple:

The Dark One only has a set amount of time to transmigrate someone after death.

And the further from Shayol Ghul the death occurs, the more time he needs to "reach" the soul and save it for transmigration.

So, balefire - due to its time reversal effect - reduced the amount of time available to save the soul, and the distance from Shayol Ghul also reduces the time available.

However, balefire on its own isn't necessarily enough to prevent transmigration - if the balefire amount is small enough, there might still be enough time to save the soul.

Similarly, great distance from Shayol Ghul on its own isn't enough to prevent transmigration either.

But the combination of balefire and distance from Shayol Ghul was enough to make it impossible to save Asmodean.

Let's say the Dark one has 10 minutes to save a soul after death.

For every 100 miles away from Shayol Ghul, he requires an extra minute to "find" the soul that has just died.

So that would mean that he can save a soul up to 1000 miles away from Shayol Ghul - given the current size of the Bore.

Let's say Caemlyn is 500 miles away from Shayol Ghul. Normally, the Dark One would be able to save Asmodean if he died there, and still have 5 minutes to spare.

But because a small amount of balefire was used to kill him, it erased an additional 5 minutes of his life, BEFORE he was actually killed.

So the distance plus the balefire meant that the 10 minutes was used up before the Dark One could save him. That's assuming the Dark One wanted to save him of course, in order to exact eternal punishment from him for his betrayal.

But the above is the logical explanation regarding why both the METHOD and the PLACE of Asmodean's death prevented his transmigration.