Bimodal stimulation, combining cochlear implant (CI) and acoustic input from the opposite ear, typically enhances speech perception but varies due to factors like temporal mismatch. Previously, we used cortical auditory evoked potentials (CAEPs) to estimate this mismatch based on N1 latency differences. This study expands on that by assessing the impact of temporal mismatch compensation on speech perception. We tested bimodal CI users in three conditions: clinical, compensated temporal mismatch, and a 50 ms mismatch. Measures included speech understanding, pupillometry, CAEPs, selective attention decoding, and parietal alpha power. Despite stable speech understanding across conditions, neural measures showed stronger effects. CAEP N1P2 amplitudes were highest in the compensated condition. Phase-locking value (PLV) and selective attention decoding improved but lacked significance. Parietal alpha power increased under 50 ms mismatch, suggesting cognitive resource allocation. Pupillometry correlated with speech understanding but showed limited sensitivity. Findings highlight that neural metrics are more sensitive than behavioral tests for detecting interaural mismatch. While CAEP N1P2 amplitudes significantly improved with compensation, other neural measures showed limited effects, suggesting the need for combined temporal and spectral compensation strategies.