A bimanual demonstration specifies both what the robot should do and one particular schedule for when each arm should act. Standard imitation learning does not distinguish task-required cross-arm constraints from incidental scheduling choices, and may therefore exploit opposite-arm progress as a shortcut cue, creating spurious cross-arm coupling even where relative timing is irrelevant for the current task phase. We introduce Constraint-preserving Temporal Recombination (CTR), a training-time data intervention that preserves recorded arm-local sensorimotor content while retiming the corresponding segments to realize admissible schedules that preserve task-required cross-arm constraints. We use CTR to train Diffusion Policy, Action Chunking with Transformers, and $π_{0.5}$, and evaluate them on four simulated and four real-robot tasks. Across six real-robot bimanual progress-state initializations, CTR raises worst-state success from 56% for the strongest non-CTR schedule mixture to 76%. With $π_{0.5}$ on an Independent task, a 4 s pause transfers 2.56 s of delay to the opposite arm under the Concurrent schedule distribution, but only 0.25 s with CTR. On real robots, CTR violates task constraints in only 0--4% of trials, versus 36--98% for narrow-schedule baselines. Code will be released at https://github.com/MINT-SJTU/CTR.

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