This fallacy is known as Post hoc ergo propter hoc and is indeed a mistake that is often made. However, there are some situations in which we can infer causation from correlation, and where the arrow of time is very useful. These methods are mostly known as Granger causality methods of which the basic premise is: X has a Granger causal influence on Y if the prediction of Y from its own past, and the past of all other variables, is improved by additionally accounting for X. In practice, Granger causality relies on some heavy assumptions, such as that there are no unobserved confounders.
Yes, @NeuroStats likes to call it “Granger prediction” for this reason