Chromosome conformation in mammals is closely related to gene regulation. Within topologically associating domains, where genomic contacts are enriched, genes tend to show correlated expression across tissues and conditions, suggesting domain-wide mechanisms coregulating multiple genes, such as enhancer sharing or local histone mark spreading. At the single-cell level, where transcription occurs in sporadic bursts, transcriptional coordination has been observed between proximal genes, but how the local folding of mammalian chromosomes influences gene coregulation in cis at individual alleles remains unclear. Using single-molecule microscopy, we imaged nascent transcription from three adjacent genes located around a strong contact insulation site at the FOS locus, during the estrogen response in human breast cancer cells. To interpret this data, we developed two new analysis approaches to dissect the sources of (co)variation in gene activities: one to separate allele-extrinsic, allele-intrinsic, and gene-autonomous components; and another one to quantify the contributions of burst co-occurrence and burst size correlations. We find that transcriptional variability is largely gene-autonomous, yet correlations between genes display distinct patterns and occur almost exclusively in cis. Correlations are stronger between proximal and less insulated genes. However, unexpectedly, substantial correlations also occur across the strong insulation site and, under certain conditions, two proximal genes on the same side can exhibit uncorrelated burst occurrences. By disentangling burst co-occurrence from burst size correlations, we reveal transcriptional patterns suggesting two distinct coregulatory mechanisms influenced by local chromosome folding.