Just purchased Time Master for my IPad yesterday. I have downloaded, printed and reviewed the manual. I also just took a look at the TM forum to see if my query was previously answered; I have not found my answer yet so here goes.
In the TM FAQ, it is mentioned that one can close the TM App and if a Time Entry is running, one should see a red circle with a number in it in the upper right of the TM icon.
I have tested this with Sessions and without sessions, i.e. leaving a time entry open and I see no red circle when I close the TM App.
Don J J Carroll