As DSpace (5.3) Administrator I don't see the task-lists (Tasks in Pool and Owned Tasks) in MySpace, although there are many not-approved (test-)submits. This happens as well in XMLUI as in JSPUI. Is there something in the configuration that can cause this behavior?
In the standard (called "traditional") workflow, tasks are assigned to members of specific workflow groups, at the time the task passes through the workflow stages. This means the specific members of a workflow group get those tasks at the time when the tasks are created.
So this is why a person suddenly won't see older tasks after he or she has been added to a specific group. This person will only get the new tasks, that are created after he or she is in the group.
This is different in the optional workflow system called "configurable workflow" that became part of DSpace 3.
https://wiki.duraspace.org/display/DSDOC5x/Configurable+workflow
For configurable workflow, tasks do remain assigned to the groups themselves, so the behaviour there is different. The main reason why configurable workflow hasn't completely replaced the old system is that right now, it is still an XMLUI only feature.