Multiple lines of evidence indicate that visual attention's temporal properties differ between the left and right visual fields (LVF and RVF). Notably, recent electroencephalograph recordings indicate that event-related potentials peak earlier for LVF than for RVF targets on bilateral-stream rapid serial visual presentation (RSVP) identification tasks. Might this hastened neural response render LVF targets perceptually available sooner than RVF targets? If so, how might the visual system reconcile these timing differences to estimate simultaneity across the LVF and RVF? We approached these questions by presenting bilateral-stream RSVP displays that contained opposite-hemifield targets and requiring participants to judge both the targets' temporal order and simultaneity. The temporal order judgments (TOJs) revealed that participants perceived LVF targets ∼134 ms sooner than RVF targets. This LVF hastening approximates a full cycle of visual attention's canonical ∼10 Hz (∼100 ms) temporal resolution. In contrast, performance on the simultaneity task did not exhibit the LVF hastening observed on the TOJ task, despite identical retinal stimulation across the two tasks. This finding rules out a stimulus-driven "bottom-up" explanation for the task-specific behavior. Moreover, error patterns across the two tasks revealed that, within the decision stage of simultaneity judgments, participants remapped LVF targets, but not RVF targets, to a later time in the RSVP sequence. Such hemifield-specific remapping would effectively compensate for the cross-hemifield asymmetries in neural response latencies that could otherwise impair simultaneity estimates.