If the universe is fully deterministic, then the future is already decided. Which means there is no difference in principle between past and future, since both are determined from the very beginning - indeed, the beginning, if it can be identified at all, cannot be distinguished from the end.
In this case the apparent order in the universe is not a product of the flow of time, which, past and present being undifferentiated in principle, is shown to be an illusion. And without a flow of time, without that linear order, cause and effect cannot by definition be distinguished from each other. What we have is correlation, configuration, order, but not cause and effect, since cause and effect are temporal phenomena.