The nature of causality is controversial, but in my opinion it should be understood as a feature of the second law of thermodynamics. That causes precede their effects is an empirical law, not a logical necessity. Time turners can violate this in certain ways, but they don't throw it out entirely.

As you look through the block universe, you can observe various features corresponding to causality: the increase in macroscopic entropy, the expansion of radiation, the human creatures inside that remember the past and plan for the future. The block universe model doesn't eliminate causality; it is a physical feature within that universe.