When I view My Tasks, it seems that any Task in the root level of the project displays a tag with the project name. But Sub-tasks do not… instead they display the name of the parent task.
Subtasks don’t automatically inherit their parent tasks tags, custom fields or project. SO unless you manually add them a tag, the tag won’t appear on the subtask itself or in your my task.
In the test I ran below, I manually added my “yellow tag” to the subtask, and you can see in the screenshot from My Tasks that it does appear in my My Tasks list!
I hope this helps, but let me know if you have any follow-up questions!