Foundation Task Plan has two related Task objects. These objects are Tasks and Process Execution (PEX). The key distinction is the Process Execution is created when running a Task or recipe in Capture Hub.
There is a known issue where a user executes a task in Capture Hub, then Task reads as a different lifecycle state in the Task Plan page. An example is a user marks a Task as complete in the Capture Hub window, but upon entering Task Plan it show the lifecycle state is in progress. What is happening is the PEX object is being marked as completed, but not the Task.
What cause the is issue is when there is a mismatch between the signature policies for the two objects. Say that moving a task into a completed state requires a signature but the PEX does not. The best way to avoid this is to make sure for each Task item that has a signature policy, the PEX item gets the same policy.
This can be managed under the Signature Policy page in the Admin and Settings in Hub. If this mismatch does happen there is another post which which explain how to fix this.