How do they run DataCare overnight? A scheduled task or a delayed job (with the workstation locked)? If the former case then it should just happen. If the latter then by definition DataCare will not close when finished.

I imagine if run by a scheduled task and DataCare does close, have the first person in the morning check the Active Users to see if DataCare closed.

I can't suggest any ways to ensure that DataCare closes while it is run unattended. DataCare and Windows and the network all have to do their thing correctly.