How do I add columns to the Workflow Tasks list, and use them?

I have a need to add 2 columns to a task list and have them populated by a workflow. Basically, I have Program Name and Project Name. These values are pulled from other lists using the "Update an Item" action and runs once a task is completed. It works fine if I create a task manually in the list. If a workflow creates a task, "Flexi-task" for example, the columns are not updated and the Program and Project workflow does not error (says completed).

What is the best way to update these columns for all tasks that are added to the list?