"What time is it?" is a deceptively simple question. Sociotemporality, or the social experience of time, is often taken for granted until there is a coordination breakdown. This dissertation explores an especially acute breakdown in time: the high-tempo, time- and safety-critical work of digital humanitarians -- teams of everyday people across the globe who curate social media and other online information for crisis responders on-the-ground during a mass emergency. Specifically, this work identifies and investigates a new concept of breakdown, coined sociotemporal disorder, across empirical, theoretical, and design constructs to understand how time is socially structured and experienced in humanitarian work; the temporal sensemaking strategies the team uses to discern information; and new ways to reveal breakdowns in time as a resource for the design of sociotechnical tools appropriated for this work. Together, this research contributes a roadmap to address a longstanding gap in the CSCW and HCI literature by interleaving the social experience of temporality with instrumented time to mitigate against sociotemporal disorder to allow distributed online work to productively unfold. This research, as a whole, foretells future work in exploring sociotemporal disorder as a resource in the design of sociotechnical systems.