It's somewhat difficult to say how Mathu truly feels about destiny vs. determination, because unlike a number of the other characters, we never get a chapter from his perspective. This means that all of his thoughts, emotions, and opinions are only relayed to the reader by other characters. However, because Mathu is the most respected character in the book, it seems we can trust his words as they appear in Rooster's chapter. In it, Mathu presents his own perspective on destiny vs. determination when he and the other black men enter into the house to talk before Mapes is set to take Mathu in.
Late in the chapter, when most of the other black men vow to remain by Mathu's side (and therefore go to jail with him, as they continue to claim responsibility for Beau's death), Mathu opens up about his feelings regarding them, saying, "I never thought I woulda seen this day," followed by a lengthy outpouring of emotion:
Till a few minutes ago, I felt the same way that man out there feel about y'all—you never would 'mount to anything. But I was wrong. And he's still wrong. 'Cause he ain't go'n ever face the fact. But now I know. And I thank y'all. And I look up to you. Every man in here. And this the proudest day of my life.
Up until this point, Mathu thinks that it is the fate of the other black men to remain cowards, to not stand up or show self-determination. Perhaps he thinks that his own destiny is to be the only one who does stand up. This suggests that he believes in fate. However, if we continue to look at what he says in the house, we see that this epiphany marks a change in his perspective:
"I been changed," he said. "I been changed. Not by that white man's God. I don't believe in that white man's God. I been changed by y'all. Rooster, Clabber, Dirty Red, Coot—you changed this hardhearted old man."
Because he outwardly denies the "white man's God" and puts the emphasis on the individuals standing for him and with him, he reveals that his perspective has shifted and he now sees the other black men as capable, competent men who are making their own choices to reshape their future and their society.