[goatlover]

A law _implies_ a causal relationship because a law is thought to model a universal relationship (B always occurs when A). How you interpret the causality depends on your metaphysics. It can be descriptive based on constant conjunction, if you're so persuaded.

Scientists will state that B happens BECAUSE of A, when A is thought to be a necessary condition for B. That's the causal implication.

[throwaway37585]

In what sense do Maxwell’s or Einstein’s field equations imply causality?

[goatlover]

In that fields interact with particles, resulting in an electric current or acceleration, for example.

[jhanschoo]

What, then, causes the phenomenon that fields interact with particles?

Historically, there has been a multitude of ideas and phenomena that have been labeled as causation. Aristotle, back then, identified four notions of causation, and the modern reader immediately will feel that some of these notions themselves are still too general. When you make a claim like "nature obeys causality", you need to be more precise in what you refer to by nature and causality, else your claim is far too ill-defined to mean much of anyting.