Many, although not all, determinists are also materialists (as Alexander King said above, for them determinism is just the corollary to the laws of physics). Since for these, there isn't really much to meta-physics, one wouldn't expect meta-physical arguments.
Within the theologic philosophy/philosophy of religion, however, there are those who are deterministic but not materialistic, so their attempts seek to explain things on a more metaphysical basis. See for example, Martin Luther's On the Bondage of the Free Will -
For if man has lost his freedom, and is forced to serve sin, and cannot will good, what conclusion can more justly be drawn concerning him, than that he sins and wills evil necessarily?
But now that God has taken my salvation out of the control of my own will, and put it under the control of His, and promised to save me, not according to my working or running, but according to His own grace and mercy, I have the comfortable certainty that He is faithful and will not lie to me, and that He is also great and powerful, so that no devils or opposition can break Him or pluck me from Him.
According to Martin Luther then, because of the nature of sin and what it's done to our souls, we are "forced to serve sin," and it is only by God's grace that we are prevented from sinning - in either case, it is not our own doing.
(A list of quotes from the work).