The talk of reduction has origins in philosophy of 20th century, Carnap and Neurath in the 1930s and especially Nagel's model of 1949, see SEP. References by scientists are second hand. It should also be said that the current mainstream is that chemistry has not been reduced to physics, although that was what earlier analytic philosophers believed, and full reducibility is implausible for structural reasons, see Chemical Reduction.

See Physical chemistry: History: The term "physical chemistry" was coined by Mikhail Lomonosov in 1752, when he presented a lecture course entitled "A Course in True Physical Chemistry".Modern physical chemistry originated in the 1860s to 1880s with work on chemical thermodynamics, electrolytes in solutions, chemical kinetics and other subjects. One milestone was the publication in 1876 by Josiah Willard Gibbs of his paper, On the Equilibrium of Heterogeneous Substances.

My guess is that it started with the development of the Periodic Table. When they found that chemical properties obeyed a pattern, it was natural to look for a correlation with physical structures.

"When and why did scientists just start assuming that chemistry is reducible to physics?" I'm not sure that 'assuming' is the right word here. Obviously, making assumptions is part of the process of science, but that's not why we care about it. That sounds almost like anti-science rhetoric. The only thing that really matters in science is what can be demonstrated. Assumptions can vary from person to person and carry little weight.

@Conifold "full reducibility is implausible for structural reasons" I feel like there's a definitional question here. If we define 'physics' to be the study of physical reality, and chemistry is the study a subset of physical reality, then trivially, chemistry is a subset of physics. In other words, chemistry is the way we approach the physics of chemicals. But what you are pointing to seems to be about whether the practice of chemistry can be accomplished with fundamental (quantum) physics which seems pedantic and even a little myopic to me.

I'm voting to close as unfocused. Chemistry has been part of physics since its emergence from alchemy and metallurgy. Before reopening, please look up legendary chemist Robert Boyle to get a sense of the historical context which marked the transition from alchemy to chemistry.

It would be good to focus the question a bit more ("reducibility" can mean a lot of different things). But I will immediately vote to re-open iif the question happens to be closed.

Dating at least back to classical Greece, physics was the study or contemplation of the generalizable principles which describe the way the natural world, both living and nonliving, changes. The English words physics and physical are derived from the Greek physis, nature, and physica, natural(ly). Are you sure that anybody ever thought of chemistry/alchemy as not being a set of particular principles whose possibly unknown generalizable principles were/would be principles of physics?

(At least insofar as they weren't principles of souls and spirits?)

Also, in case you weren't aware, there is a History of Science and Math Stack Exchange, which might get you interesting answers to a similar question expressed differently.

-1, did not do basic research before posting.

@Graham, a more perspicacious reader might have noted my description of 19th century medical experiments and realized that it was my research into the history of science that led to this question.

@JimmyJames Reduction is not about using quantum physics to do chemistry in practice, but it takes more than trivialities about subsets of physical reality. The laws governing those subsets should reduce, whether it is practical to track that or not. That chemicals are made of physical parts does not imply that laws governing physical parts induce chemical laws (in full), that is not trivial at all. Known 'derivations' of chemical laws from quantum physics import some macroscopic considerations by hand rather than derive them from microphysical ones, and hence are circular as reductions.

@Conifold I think you are missing my point. If we assume for a second that chemistry cannot be fully described by QM (something I have no qualms with considering or accepting with evidence) that doesn't mean chemistry is not a subset of physics. It simply means there's something else required to describe it. Unless, that is, you are saying chemistry is some sort of supernatural phenomenon, and I don't think you are.

I feel compelled to mention XKCD 435 "Purity" which nicely captures this ladder of understanding, with physics purportedly at the bottom, the standing of which is then contested by mathematics. Interestingly philosophy brackets the top and bottom of the ladder.

@JimmyJames Your point is strange, why would people care to debate whether to call something "subset of physics" or not? The standard meaning of reducibility that this question asks about has little to do with that and is not vacuous. It is whether higher order laws (chemical, biological, etc.) simply repackage fundamental laws or "emerge" over and above them. Do some chemical laws manifest only at the macroscopic level with nothing in fundamental physics giving rise to them or are they its consequences. That is what both physicalists and their opponents care about, not verbal choices.

@Conifold "It is whether higher order laws (chemical, biological, etc.) simply repackage fundamental laws or "emerge" over and above them." I argue that anything that cannot be reduced to some set of existing fundamental laws is in fact a fundamental law. For example, from your link above, there's a really good example "dimethyl ether and ethanol share a Hamiltonian" yet are empirically different chemicals. If true, this is incontrovertible proof that the Hamiltonian is not sufficient to describe chemicals and there's some other fundamental factor that is missing.

@Conifold Sorry, I also want to address this "Your point is strange, why would people care to debate whether to call something "subset of physics" or not?" I don't think it's a debate. If you (as I do) think that physics is the study of the nature of physical reality and also believe (as I do) that chemistry is about physical reality, then it's simply a tautology that chemistry is a subset of physics. Arguing that something can't be reduced to what it is makes no sense.