The answer to this question can be found in the latest book Warheart. At least, I believe the information gives us an answer as to why it happened as it did. The full explanation spans an entire chapter, but I will summarize some key bits of information from the book.
Warheart, Chapter 29, page 209: "Hannis Arc is the one who gave Darken Rahl the last box of Orden." Khalan said, trying
to keep track of it all in her head. "You mean he did it that to help
start this prophecy to unfold? The prophecy he plays a central part in
and that he would benefit from?"
[Richard replied] "Exactly. he has been moving the pieces around like pieces on a chessboard in order to bring about the events the
scrolls talk about. Its as if he sees prophecy of himself doing these
things, and then does them to make the prophecy reality.
"He wanted to open this gateway through this spectral fold, because he needed Sulachan's help to conquer the world
of life, so he put the boxes in play by giving the third box of Orden
to Darken Rahl He was making moves that would have repercussions later
on, all down the line. He knew from the scrolls that giving Darken
Rahl the last box he needed to put them in play would trigger events
in prophecy. Unlike us, he knew from the scrolls what the power of
Orden really was.
"Hannis Arc was moving a pawn, knowing from prophecy that if the boxes were in play, I would defeat Darken Rahl and therefore go on to
become the Lord Rahl leading the D'Harian Empire that would then be
drawn into the war against the Imperial Order.
"He knew that I would use the power of Orden to end the war with the Imperial Order, which is a part of the larger great war that
Sulachan started so long ago. After all, Sulachan created the dream
walkers. Emperor Jagang was a descendant of those dream walkers
created by Sulachan so that he would start the war that I would end by
using the power of Orden that Hannis Arc would then use, once the star
shift weakened the veil, to bring Sulachan back from the dead."
Kahlan pressed her hands to her head. "Dear spirits. And they were using this knowledge of the use of Orden all along?"
Richard nodded. "Hannis Arc had already moved that pawn long ago by giving the box to Darken Rahl to begin the chain of events that
would eventually get me to use Orden's power, because he didnt have
the key to it, but the scrolls said I would, which would in turn get
him what he was ultimately after: to be the ruler of the world of
So basically, what this is telling us is that Hannis Arc orchestrated this all, to fullfill his ultimate goal. Darken Rahl set the boxes in play "early" because he was destined to, is the simple answer. The more complicated answer may not be able to be found exactly, but his character and need for power are most likely what drove him to put the boxes into play "early".
It even goes a tad further than this.
Warheart Chapter 29 pg 215 Richard Rahl : "...Sulachan sent the prophecy to this world, through prophets in this world, so that they would write it in the scrolls, so that Hannis Arc would read it and initiate it all by putting the boxes of Orden in play. It is all part of Sulachans grand plan."
So, that means
Sulchan was actually the reason for everything, including the boxes of Orden being put into play. Darken Rahl was really just a tool, he was the key to "activating" Richard since Richard has the key to the boxes of Orden.
We could even take this a step further, in effort to try and answer the real question as directly as possible. Darken Rahl traveled the underworld, as your quote points out.
Sulachan was the king of the underworld as he was called in the book, and had his hands in everything in the underworld
So its quite possible he even influenced Darken Rahl to use the boxes "early" or at just the right time, to make the events happen as they needed to.
Though there is no direct evidence of them meeting or talking, Sulachan influenced all of prophecy from the underworld through spirits and Darken Rahl interacted with alot of spirits, so any information or actions Darken Rahl took because he "got information from the underworld" could be credited back to Sulcahan's manipulation.
But that part is specualtion.