"Determinism" seems closer to it; though perhaps many of them believed that humans had souls that were exempt from the physical laws of nature--so, "physical determinism"?

Science is also possible in a non-deterministic universe, one in which the evolution of physical systems has a random component and the future is not fully predictable from a full knowledge of the present. All science needs are natural laws, repeated regularities; they don't have to be entirely deterministic. And in fact scientists did not have a strong reason to think the universe is deterministic until they had what looked like a complete set of the laws of physics, in the nineteenth and twentieth centuries.

On the other hand, a god that does miracles is incompatible with natural law as we know it, because we presumably can't put an upper limit on the probability of a miracle occurring. An intelligent god can selectively cause miracles to disrupt particular experiments or to lead scientists to a false conclusion. Science pretty much assumes that won't happen.

Many of them would have insisted there the lawfulness of Nature was tied to the existence of a Lawgiver, and that theism and science fit together harmoniously in a unified worldview, not in separate mental boxes.

"Many" is ambiguous. What place and time are we talking about? I would expect that until, say, the 19th century, the majority of scientists everywhere were conventionally religious.