Digital banking adoption in Small Island Developing States (SIDS) faces unique cultural and technological challenges, such as limited digital literacy, infrastructure deficits, and socioeconomic disparities. This paper introduces the Technological Influence on Digital Banking Adoption (TIDiBanD) Framework, a novel approach to contextualizing how backend technologies, data assurance practices, and frontend innovations interact with cultural barriers in digital banking adoption. The framework provides researchers with a structured method to examine the influence of technologies such as social robots, intelligent virtual assistants (IVAs), and generative AI tools in fostering digital banking acceptance. To demonstrate the utility of TIDiBanD, we conducted an empirical study evaluating the persuasiveness of social robots and IVAs in promoting digital banking services in a SIDS population. Results indicate that while IVAs were perceived as more competent and easier to interact with than social robots, social robots evoked stronger positive emotions. The study also finds that consumers in that state may prefer familiar technologies over novel ones for financial interactions, highlighting the need for culturally aligned digital banking strategies. These findings provide actionable insights for banks and policymakers aiming to enhance digital financial inclusion through persuasive technologies.