According to the user guide, The My instances tab, shows all the process instances where you currently have an uncompleted user task.
This would mean that if I start a process programatically, then claim the first task, it would show up in the my instances tab. This is not correct. Furthermore, processes that were started but not claimed ARE visible (I do not have an uncompleted user task there). In fact, it seems the instances are shown that have been created using the "start process" button on the definitions tab.
I suspect the "my instances" in fact shows processes started by me. But because the programatic way does not require a log in, these processes are not shown.