We were facing an issue where a process triggered from Studio Web creates a task in Action Center, but only the user who runs the process is able to access the task. Even when we tried to assign the task to a specific user using the Assign Task activity, the activity executes successfully without any errors; however, the task was not actually assigned to the intended user.
The Resolution was to use the Exact ‘User Name’ or ‘Email ID’ displayed on the 'Admin>Accounts & local groups>User accounts’.
It is Case Sensitive.
I think this should be taken care, as it is not throwing error too.