Hi Clint,
Task queues run server side asynchronously, so if you want to perform an action once a task has completed, I believe the only option at the moment is that you would need to add some meta-data and logic to record when the task had completed and then poll within the client to refresh the page.
Another option is to leverage System.ProcessedQueueTask this contains all completed tasks and includes the microflow name and arguments, so you could query this entity to determine when your task had completed
https://docs.mendix.com/refguide/task-queue/