Allopolyploidy involves the hybridization of two evolutionary diverged species and the doubling of genomic material. Frequently, allopolyploids exhibit genomic rearrangements that recombine, duplicate, or delete homoeologous regions of the newly formed genome. While decades of investigation have focused on how genome duplication leads to systematic differences in the retention and expression of duplicate genes, the impact of genomic rearrangements on genome evolution has received less attention. We used genomic and transcriptomic data for six independently resynthesized, isogenic Brassica napus lines in the first, fifth, and tenth generation to identify genomic rearrangements and assess their impact on gene expression dynamics related to subgenome dominance and gene dosage constraint. We find that dosage constraints on the gene expression response to polyploidy begin to loosen within the first ten generations of evolution and systematically differ between dominant and non-dominant subgenomes. We also show that genomic rearrangements can bias estimation of homoeolog expression bias, but fail to fully obscure which subgenome is dominantly expressed. Finally, we demonstrate that dosage-sensitive genes exhibit the same kind of coordinated response to homoeologous exchange as they do for genome duplication, suggesting constraint on dosage balance also acts on these changes to gene dosage.