As the construction industry increasingly adopts digital technologies, recent studies emphasize digital twins as essential tools for managing construction projects and automating workflows. Although research has advanced the technical aspects of digital twins, there is a notable gap in examining human performance factors, particularly situation awareness-a cognitive process crucial for recognizing, comprehending, and anticipating changes in the work environment. With greater reliance on automation, neglecting this critical capability can lead to severe oversights, particularly during disruptions. To address this gap, we conducted a qualitative study grounded in a theoretical framework to explore the situation awareness requirements under different disruption scenarios in two contrasting construction contexts: offsite production and onsite assembly. First, drawing on 16 semi-structured interviews and non-participant field observations, we employ goal-directed task analysis to reveal the distinct information needs in each context. Second, through a comprehensive content analysis of the interview narratives, we identify the dynamics of gaining and maintaining situation awareness and provide digital twin design recommendations. Findings indicate that managers must shift from a macro-level overview to a micro-level detail in offsite production, requiring digital twin displays with adaptable granularity. In contrast, onsite assembly demands an intensely iterative approach to situational awareness, which calls for comprehensive real-time digital twin displays that support quick back-and-forth assessments. This study contributes by formalizing experts' background knowledge, which can serve as a valuable basis for creating context-sensitive digital twin systems that better support human decision-making in offsite construction contexts and beyond.