The biochemical processes for A. oryzae inhibiting the growth of B. cereus involves the production of a range of metabolites that exert antimicrobial properties [1,2,3,4]:
"The exAP-AO17 protein strongly inhibited pathogenic microbial strains, including pathogenic fungi, Fusarium moniliform var. subglutinans and Colletotrichum coccodes, and showed antibacterial activity against bacteria, including E. coli O157 and Staphylococcus aureus."  Park et al.
"Besides its potent secretion machinery, A. oryzae is a generous source of various secondary metabolites [...]. Many of the metabolites secreted by A. oryzae have different reported bioactivities such as anticancer, cytotoxicity, antimicrobial, antihypertensive, and antiviral activities (Table 2)."  Daba et al.
Table of metabolites from Daba et al.
A mutated strain of A. oryzae also produced an unknown compound with antimicrobial effect, suggesting antimicrobial potential outside of the stable domesticated strains:
"Over 3000 EMS-treated, putative mutant A. oryzae cultures were tested in the described screening assay for antibacterial activity. A single EMS-treated A. oryzae isolate, named CAL220, exhibited antibacterial activity in the screening assay as indicated by complete lack of visible MRSA growth in the assay."  Leonard et al.
As you're aware, Koji itself is an inoculum rich in enzymes for further fermentation of soy and grains, but also contains easily digestible sugars derived from A. oryzae breaking down the rice . Combined with the near-neutral pH (>6) throughout and increasing at the end of fermentation , Koji would be very hospitable to B. cereus without the antimicrobial metabolites. As only a relatively small amount of Koji is used for the second stage of fermentation, the concentration and effect of these metabolites is diluted, hence the need for added salt for pathogen inhibition for this stage.
Figure of pH over time from Chancharoonpong et al.
Given the innumerable regional strains of A. oryzae in koji manufacture, and other species of fungi involved, there are countless other undocumented metabolite compounds that we're only beginning to identify - and biochemists outside of the
field of food technology are very interested in these as well. 
But to simplify things, yes, there is a single (group of) biochemical process responsible for A. oryzae outcompeting B. cereus, and it's the production of antimicrobial compounds.
 Isolation and Characterization of an Extracellular Antimicrobial Protein from Aspergillus oryzae.
Seong-Cheol Park, Nae Choon Yoo, Jin-Young Kim, Hae Kyun Park, Byung Jo Chae, Song Yub Shin, Hyeonsook Cheong, Yoonkyung Park, and Kyung-Soo Hahm.
 The ancient koji mold (Aspergillus oryzae) as a modern biotechnological tool.
Ghoson M. Daba, Faten A. Mostafa & Waill A. Elkhateeb.
 Random Mutagenesis of the Aspergillus oryzae Genome Results in Fungal Antibacterial Activity.
Cory A. Leonard, Stacy D. Brown, and J. Russell Hayman.
 Fermentation and the microbial community of Japanese koji and miso: A review.
Joanne G. Allwood Lara T. Wakeling David C. Bean.
 Enzyme Production and Growth of Aspergillus oryzae S. on Soybean Koji Fermentation.
Chuenjit Chancharoonpong, Pao-Chuan Hsieh, Shyang-Chwen Sheu
 Medical Application of Substances Derived from Non-Pathogenic Fungi Aspergillus oryzae and A. luchuensis-Containing Koji.