Let me first acknowledge that Belusov published very little, and what he did publish is hard to get a hold of in English, so this answer is not based on any specific writing of his, but rather is speculation based on what other scientists were doing at the time.
In those days, it was quite difficult to study enzyme-catalyzed reactions, because the structures of the active sites and even the identity of most of the relevant residues were generally unknown. Obviously, techniques such as recombinant overproduction systems and targeted mutagenesis were not available.
In this environment, cofactor-dependent enzymes (including metalloenzymes) were of particular interest because it was presumed that in those enzymes, the catalytic function might be primarily provided by the cofacter, and the role of the protein might be as simple as just providing a scaffold for the cofactor and a binding pocket to bring the substrate to it. If that were true, then it might be possible to mimic the enzyme and effect catalysis with a much simpler system consisting of the cofactor bound to a small scaffold or even free in solution. As an example, pyridoxal was found to catalyze a wide variety of reactions by itself in solution, albeit with slower rates and much less specificity than enzyme-bound pyridoxal phosphate.
The benefit of these simplified systems is that it is much easier to probe the reaction mechanisms, though with the caveat that the mechanism might not be the same as when the reaction happens on an enzyme.
In the case of Belusov, it had been observed that a number of the enzymes in the Krebs cycle are metalloenzymes, including the first two reactions from citrate, ie those catalyzed by aconitase (with an iron-sulfur cluster) and isocitrate dehydrogenase (with a Mn(II) ion). It is likely that Belusov was mixing citrate with different metals in the hopes of reproducing one or both of these reactions in a non-enzymatic system with the goal of furthering the understanding of the reaction mechanisms and the role of the metals.