"There is no ground to assume the continuity of causation or motion...without taking for granted that things will be tomorrow as they have been today."

I'd contend that is an epistemological assertion, not a metaphysical one.

Our ability to do physics and metaphysics alike depends on our epistemology.

The Aristotelian distinction worth keeping in mind is physics is the study of that which is real and changes, while metaphysics is the study of that which is real and is unchanging.

With that distinction, it seems clear to me that, while our metaphysics can color our understanding of physics, our ability to study changing things does not wholly depend on whether we have a correct metaphysics.