Tropical cyclones (TCs) displace millions every year. While TCs pose hardships and threaten lives, their negative impacts can be reduced by anticipatory like evacuation and humanitarian aid coordination. In addition to weather forecasts, impact forecast enables effective response by providing richer information on the numbers and locations of people at risk of displacement. We introduce a fully open-source implementation of a globally consistent and regionally calibrated TC-related displacement forecast at low computational costs, combining meteorological forecast with population exposure and respective vulnerability. We present a case study of TC Yasa which hit Fiji in December 2020. We emphasise the importance of considering the uncertainties associated with hazard, exposure, and vulnerability in a global uncertainty analysis, which reveals the full range of possible outcomes. Additionally, we perform a sensitivity analysis on all recorded TC displacement events from 2017 to 2020 to understand how the forecast outcomes depend on these uncertain inputs. Our findings suggest that for longer forecast lead times, decision-making should focus more on meteorological uncertainty, while greater emphasis should be placed on the vulnerability of the local community shortly before TC landfall. Our open-source codes and implementations are readily transferable to other users, hazards, and impact types.