Online reasoning video segmentation (Online RVS) requires a model to segment query-referred objects as a video streams in, using only the frames observed so far. Existing formulations largely assume a fixed target set throughout the video, overlooking a fundamental property of streaming reasoning: as new events occur, the objects that satisfy a query may change over time. To address this, we propose a new task, Generalized Reasoning Video Segmentation (GRVS), where the target set depends on query-relevant events accumulated over the observed video history. As new evidence accumulates, the target set can evolve from empty to one or multiple objects, requiring a model to continuously maintain target validity while localizing the valid objects currently in view. To evaluate GRVS, we build Isekai, a diagnostic benchmark of 60 videos and 197 queries across 11 temporal query families, with 12,569 scoring points whose target sets are causally annotated over time. We further propose Sekai, an online framework with two complementary components: an Event Memory Reasoner (EMR) that maintains query-relevant events and evolving target states in structured memory, and a Memory-Grounded Decoder (MGD) that identifies valid targets from this memory and localizes them in the current frame. Experiments show that Sekai significantly outperforms existing online RVS methods, achieving 50.33 J&F and improving over the strongest baseline by 3.2 points. Code, example annotations, and evaluation scripts are available at https://github.com/zenastangbi/Sekai.

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