I have heard a suggestion that perhaps the different tone is meant to indicate יחושע's ענוה. But I am not convinced. In pondering this issue I did come to an interesting discovery which may somehow be connected to the reasoning behind this. Of all of the sons of יעקב, the only one whose name is pronounced with the accent not on the last syllable is אפרים! Perhaps this affects how the פסוק needs to be noted.
As is often the case here, MG comes to the rescue:
Basically, this posuk is an exception because "Bin-Nun" is a "short" word (all the other names have more syllables). Because of that, we don't want to place a tipcha (pause/melech)immmediately prior, since that presents a slightly difficult flow of words. So we must have a mercha there, as that is the only possible meshares for a sof-posuk. Thus the tipcha (which is required to be in every single posuk at least once) gets moved to the word "Efroyim".
