Critical systems, such as those used in healthcare, defence, transportation, and disaster management, require rigorous requirements engineering to ensure safety and reliability. However, this rigour has traditionally focused on technical assurance, with less attention to the human and social contexts in which these systems are used. This paper argues that human-centricity is an essential dimension of dependability and presents a human-centred requirements engineering process for making vulnerable-user needs explicit and traceable from inclusive design guidelines to requirements, prototype features, and validation evidence. Drawing on a structured review of inclusive design literature, we identified 62 guidelines relevant to four vulnerable communities: older adults, low-digital-literacy users, rural users, and colour-blind users. These guidelines were translated into a catalogue of 67 functional and non-functional requirements for inclusive early warning systems. To our knowledge, this is one of the first studies in software engineering to consolidate and empirically validate inclusive design requirements for disaster early warning systems, where accessibility and usability failures can have serious safety consequences. The requirements were operationalised through an adaptive disaster early warning prototype and evaluated through six interviews and eight cognitive walkthroughs. The evaluation provided strong positive evidence across the four vulnerable groups, with particularly encouraging results for elderly and rural users, whose requirements achieved full validation coverage and high positive validation rates. The paper concludes by positioning human-centricity not as an ethical add-on, but as a traceable quality concern in the design of safe and equitable critical systems.