Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) plays an important role in breast cancer screening, tumor assessment, and treatment planning and monitoring. The dynamic changes in contrast in different tissues help to highlight the tumor in post-contrast images. However, varying acquisition protocols and individual factors result in large variation in the appearance of tissues, even for images acquired in the same phase (e.g., first post-contrast phase), making automated tumor segmentation challenging. Here, we propose a tumor segmentation method that leverages knowledge of the image acquisition time to modulate model features according to the specific acquisition sequence. We incorporate the acquisition times using feature-wise linear modulation (FiLM) layers, a lightweight method for incorporating temporal information that also allows for capitalizing on the full, variables number of images acquired per imaging study. We trained baseline and different configurations for the time-modulated models with varying backbone architectures on a large public multisite breast DCE-MRI dataset. Evaluation on in-domain images and a public out-of-domain dataset showed that incorporating knowledge of phase acquisition time improved tumor segmentation performance and model generalization.