Many staff and students in higher education have adopted generative artificial intelligence (GenAI) tools in their work and study. GenAI is expected to enhance cognitive systems by enabling personalized learning and streamlining educational services. However, stakeholders perceptions of GenAI in higher education remain divided, shaped by cultural, disciplinary, and institutional contexts. In addition, the EU AI Act requires universities to ensure regulatory compliance when deploying cognitive systems. These developments highlight the need for institutions to engage stakeholders and tailor GenAI integration to their needs while addressing concerns. This study investigates how GenAI is perceived within the disciplines of Information Technology and Electrical Engineering (ITEE). Using a mixed-method approach, we surveyed 61 staff and 37 students at the Faculty of ITEE, University of Oulu. The results reveal both shared and discipline-specific themes, including strong interest in programming support from GenAI and concerns over response quality, privacy, and academic integrity. Drawing from these insights, the study identifies a set of high-level requirements and proposes a conceptual framework for responsible GenAI integration. Disciplinary-specific requirements reinforce the importance of stakeholder engagement when integrating GenAI into higher education. The high-level requirements and the framework provide practical guidance for universities aiming to harness GenAI while addressing stakeholder concerns and ensuring regulatory compliance.