I worked at the same tower where atcman trained. Here's a little better screenshot of the Tower Display Monitor (TDM).
I took that picture before STARS was comissioned at PIT which is why it says WKST FAIL in the Status Info Area on the lower left, it's also why there are no targets on there. We also never ran with the labels up, they were just for educational and tour purposes only.
My preference when I was working in the tower was to assign reporting points to surface area transition aircraft, one of which was usually "...report clear of class Delta." For itinerant departures I really preferred them not
to report clear, especially during a departure push like when Pan Am would empty the ramp every hour and a half. Extra reports like that would just have added to frequency congestion.
Even after we got the CTRD I would still assign reporting points to all aircraft (except departures), partly because of the non-radar techniques that I learned in my initial training, and partly as sort of a memory-jog.
I think the general rule with VFR towers is, if they want you to report it, they'll ask you to.