Ah. So no use in real-time if there is an unplanned delay as the map will show that the train just went past you when in fact it didn't. Shame.
As far as I understand the technologies (and I assume that Berlin does the same thing as every other city-user), a precise ("physical") GPS position is usually not reported (although newer systems do that as well), but a position at a "logical" map is. In case of buses, this usually means "left the previous stop at $xx:$yy, with $zz seconds of delay; reported average speed is normal for this area, so expected arrival is at $aa:$bb." In case of trains, the usual reported data is "has left section of track $AA, is now at $BB, delay $x seconds, expected at $CC in $yy:$zz".
Not millisecond-perfect, but fairly precise to about a minute or two; the biggest guesstimate is the exact position (you'll see that all the trains seem to be using a single track, where in reality they would be on different ones).
So, while delays are reported near-realtime (and thus the scenario you describe doesn't happen), the map might be inaccurate if the route needs to be changed (e.g. there's an accident blocking the road and a bus needs to take the next street instead). Again, with the rollout of GPS-equipment across fleets, this becomes less of an issue. Btw, most delays are unplanned ;)
The L train in New York is an example of where this is installed. My understanding is this means the two staff on the train are redundant; the driver pretty much just provides acknowledgement to the train to keep doing its thing, and the conductor only opens and closes doors and makes announcements (if that). They would run with only a single staff member except for union rules.
However, even when the position of the train is known precisely (no need for fancy CTBC, just start counting wheel revolutions from a known starting point and reset any measuring error at the next known-good point, usually a station - which is the basic way the Parisians do it with their driverless metro lines), not every transport agency exposes this sort of raw data to the general public; usually it's watered down to "it's between Station A and Station B, with X seconds of delay."
FWIW, automation is actually mostly tangential to absolute v. moving block signalling. As far as I'm aware, most automated systems still use absolute block signalling.
On other lines, my understanding is that the signalling system doesn't know which train occupies a block, just that a train occupies the block. Which block is occupied isn't sent to a central control center either.
So "there's a Brooklyn-bound train 2 stops away" is the best it can do, since it can know based on which side of the tracks the train is on where the train is going. It can't know the letter or number.