Universities, departments, and research labs generate annual, end of year reports that highlight the achievements and milestones for the year, such as grants awarded and publications. Publications are items affiliated with the university or research lab and will typically include peer review papers, book chapters and books, and conference proceedings. These form metrics that contribute to departmental and university reputation and research output, which are then weighted against other research institutions to determine institutional standing within the academic sector. Therefore, research labs, departments, and universities as a whole will encourage publishing in international, high impact, and highly cited journals. These metrics reflect the research performance of the university, which can indirectly influence performance of individual academics by improving the reputation and outreach of the university as a workplace. So, yes, they do care.
Practical example for Life Sciences
Life Sciences departments at universities most likely share similar objectives and thus generate similar metrics to departments in other fields, as universities will use these criteria to generate their annual publication metrics and research output. For example, the University of Melbourne publishes an annual ‘Research Review’ highlighting outstanding research achievements from departments within the university (http://publications.unimelb.edu.au/docs/2013-Research-Review.pdf). These reports showcase the academic output and international impact of research from the university to the academic and higher education community, as well as the public. Therefore, as an author, publishing in high impact, international journals is encouraged because it improves the status of the department and university as a whole.