Improving the interpretability of phase-picking neural networks remains an important task to facilitate their deployment to routine, real-time seismic monitoring. The popular phase-picking neural networks published in the literature lack interpretability because their output prediction scores do not necessarily correspond with the reliability of phase picks and can even be highly inconsistent depending on how we window the waveform data. Here, we show that systematically shifting the waveforms during training and using an antialiasing filter within the neural network architecture can substantially improve the consistency of the output prediction scores and can even make them scale with the signal-to-noise ratios of the waveforms. We demonstrate the improvements by applying these approaches to a commonly used phase-picking neural network architecture and using waveform data from the 2019 Ridgecrest earthquake sequence.