Inspired by recent experiments on the effects of cytosolic crowders on the organization of bacterial chromosomes, we consider a feather-boa type model chromosome in the presence of non-additive crowders, encapsulated within a cylindrical cell. We observe spontaneous emergence of complementary helicity of the confined polymer and crowders. This feature is reproduced within a simplified effective model of the chromosome. This latter model further establishes the occurrence of longitudinal and transverse spatial segregation transitions between the chromosome and crowders upon increasing crowder size.