Image manipulation localization combines semantic structure with forensic traces to identify modified pixels. Within-branch spatial mixing and RGB-guided cross-branch mixing can produce different messages when composed in opposite orders. We propose OCBI, an extension of Co-Transformers that models the discrepancy between these two composition orders for localization. A local cross-branch fusion module uses the commutator of RGB-guided cross-attention and forensic self-attention to add a learnable signed correction to feature transfer. Pixelwise adaptive multiscale aggregation then combines spatial contexts before prediction. OCBI uses the Co-Transformers backbone and supervision. We compare OCBI with retrained Co-Transformers using CASIA-only task training, a 50-epoch budget, and final-epoch evaluation. Across five clean test datasets, OCBI achieves a macro PixelF1 of 0.5773, exceeding the baseline by 0.43 percentage points. Under JPEG compression, Gaussian blur, and resizing on three datasets, its average PixelF1 over 21 dataset-transformation conditions exceeds the baseline by 0.95 percentage points.