Video-based human-object interaction (HOI) understanding requires both detecting ongoing interactions and anticipating their future evolution. However, existing methods usually treat anticipation as a downstream forecasting task built on externally constructed human-object pairs, limiting joint reasoning between detection and prediction. In addition, sparse keyframe annotations in current benchmarks can temporally misalign nominal future labels from actual future dynamics, reducing the reliability of anticipation evaluation. To address these issues, we introduce DETAnt-HOI, a temporally corrected benchmark derived from VidHOI and Action Genome for more faithful multi-horizon evaluation, and HOI-DA, a pair-centric framework that jointly performs subject-object localization, present HOI detection, and future anticipation by modeling future interactions as residual transitions from current pair states. Experiments show consistent improvements in both detection and anticipation, with larger gains at longer horizons. Our results highlight that anticipation is most effective when learned jointly with detection as a structural constraint on pair-level video representation learning. Benchmark and code will be publicly available.