In my experience, this is the way SEPTA operates. Which, if you think about it, means that even when trains are “on time”, they are still late by any other system’s measure. For example, Amtrak runs the way you would expect: trains leave at the time scheduled, rather than arrive at the time scheduled. Bear in mind that Amtrak and Septa are both housed in Philadelphia’s 30 Street Station. It’s not like SEPTA exists in some vacuum.
This is ignoring the strange way they handle late trains on their track displays: to simply add the minutes as they pass by, then suddenly jumping up to 18 minutes late once they get to around 10 minutes, so the train can arrive ‘early’ at 13 minutes late.
I’ve heard that late trains only get later. This means that once a train is late, it is then given lower priority than on-time trains, so the late train’s lateness doesn’t ripple outward to other trains. So what happens when all of your trains run late?