Deep learning technologies have revolutionised pedagogical techniques in recent years by enabling individualised, adaptive learning environments in English for Specific Purposes (ESP) training. The efficacy of these AI-driven systems depends on how well they align with students' cognitive learning styles, including visual, introspective, and kinesthetic styles, which influence how they process and interact with information. This study examines the impact of cognitive learning styles on student performance and perceptions in deep learning-based ESP classes. Through stratified random sampling, 240 undergraduate students from Universitas Muhammadiyah Gresik participated in the study, which used a mixed-methods explanatory sequential design. Validated tools to evaluate cognitive styles and ESP performance were used to collect quantitative data, while semi-structured interviews with a purposive subsample provided qualitative data. Visual learners performed significantly better than their reflective and kinesthetic peers, as indicated by structural equation modeling (β = 0.42, p < 0.001). The results of a qualitative study showed that visual learners preferred graphical input, reflective learners needed depth and timing, and kinesthetic learners expressed disengagement from static interfaces. Emotional responses, including anxiety and a decline in self-efficacy, emerged as a recurrent pattern among non-visual learners. The study concludes that cognitive congruence has a critical role in determining affective participation and academic success in AI-mediated ESP situations. By emphasising the need for inclusive instructional design that considers a range of cognitive profiles, these discoveries contribute to the discussion of customised learning in digitally enhanced language training.