The future of scholarly research will be based on open data to ensure accountability, transparency and independent replication (e.g. Warren et al, New Engl J Med 2016). Thus, we need to be ready for similar scenarios.
Do I just need to cite the data source in my manuscript or will I also need to contact the authors to let them know I am using their data or to ask for permission?
Unless there is an explicit policy you need to follow (quite uncommon indeed), you just need to provide the precise citation to what you accessed. However, contacting the authors could be a smart choice: they could provide you additional data or collaborate with you more actively.