I'm also trying to use subtasks but have the same problem in Today view. I use that view every day and only use My Lists to organize and create. Since the method of use is to check off a completed task, it stands to reason the same would apply to subtasks. It's a silly oversight that it's not instantly available in Today, but is in My Lists. Just stating there are subtasks isn't as useful as displaying them to be checked off. Additionally, when I enter details, then scroll down to subtasks, checking them doesn't produce a filled circle but a dimmed or greyed-out text. It does remove the subtasks from my main task in Today, though.
Also, I create many tasks to repeat along with the subtasks. The subtasks do not seem to repeat, though. To add them back after I check the main task is a very weird process. If I go into My Lists to locate the next repeated main task, there are no subtask drop-downs but in details, under subtasks, they are still there with filled in circles. I unchecked them, added a new blank task and saved. Then, the subtasks appeared in my next repeat. I may as well not use the subtask list for "checking off" but just to view.
Regardless of that strange quirk, the subtasks need to appear on the Today view under the main task.