The mechanism underlying the spatiotemporal chromosome organization in Escherichia coli cells remains an open question, though experiments have been able to visually see the evolving chromosome organization in fast- and slow-growing cells. We had proposed [D. Mitra et al., Soft Matter 18, 5615 (2022)1744-683X10.1039/D2SM00734G] that the DNA ring polymer adopts a specific polymer topology as it goes through its cell cycle, which in turn self-organizes the chromosome by entropic forces during slow growth. The fast-growing E. coli cells have four (or more) copies of the replicating DNA, with overlapping rounds of replication going on simultaneously. This makes the spatial segregation and the subsequent organization of the multiple generations of DNA a complex task. Here, we establish that the same simple principles of entropic repulsion between polymer segments which provided an understanding of self-organization of DNA in slow-growth conditions also explains the organization of chromosomes in the much more complex scenario of fast-growth conditions. Repulsion between DNA-polymer segments through entropic mechanisms is harnessed by modifying polymer topology. The ring-polymer topology is modified by introducing crosslinks (emulating the effects of linker proteins) between specific segments. Our simulation reproduces the emergent evolution of the organization of chromosomes as seen in vivo in fluorescent in situ hybridization experiments. Furthermore, we reconcile the mechanism of longitudinal organization of the chromosomes arms in fast-growth conditions by a suitable adaptation of the model. Thus, polymer physics principles, previously used to understand chromosome organization in slow-growing E. coli cells also resolve DNA organization in more complex scenarios with multiple rounds of replication occurring in parallel.