Time-varying bivariate fields arise in many scientific applications, yet their feature-level temporal analysis remains challenging because bivariate features are not captured by scalar-field extrema, level sets, or contour-trees. Reeb spaces provide a topological representation of bivariate fields, but using them for temporal analysis is difficult: computed sheets can be noisy, their range-space projections may overlap, and meaningful correspondences across timesteps are nontrivial to define. Existing continuous-scatterplot-based approaches provide useful timestep-level summaries, including descriptors of domain-segmentation-driven peeled CSP layers, but they do not directly provide a topological feature graph for tracking individual bivariate features. We propose a Reeb-space-based framework for tracking bivariate features over time. At each timestep, we compute the Reeb space, extract prominent sheets by area, and estimate correspondences between sheets in adjacent timesteps using complementary similarity measures in the domain and range. We summarize the resulting temporal correspondences using a Sankey-based sheet evolution summary linked with sheet, fiber-surface, and diagnostic views. We evaluate the method on two synthetic torus datasets and three time-varying molecular electronic-structure datasets. The results show that Reeb-space sheet tracking reveals persistent feature families, abrupt reconfiguration intervals, and disagreements between domain- and range-based similarities that are difficult to identify from temporal descriptors of peeled CSP layers. Overall, the framework demonstrates that Reeb-space sheets can serve as trackable topological features for time-varying bivariate data.