If someone has both an advisor and an employer role in Workday, will they be able to filter their inbox to only show tasks that are relevant to one of those roles?

You will see notifications from both HR/Finance and Student in your inbox since Workday is just one system. However, personal inbox filters can be created, just not by security role. You will need to create granular filters to fit your needs based on your advisor and employer/supervisor roles. More information on this will be provided in training.