I was at Wimbledon yesterday and had a good look at what was happening.
A correction to my earlier post - there is no countdown in minutes on the station describer. There is only destination and platform number.
So when I arrived, the first train on the station describer (I assumed it was the first as it was listed at the top) showed "City via Victoria Plat 1".
But at platform 1, the train sitting there showed "Edgware Road".
Then I walked all the way to the first carriage. The good news is that LU is well aware of this issue. There is a notice on the white Train Operator's information board, suggesting to make manual announcements due to the inaccurate station describers.
So everyone was onboard the train at Platform 1 as it was supposedly the next train to depart. I saw our driver (Platform 1 train) have a quick chat with the driver of the Platform 2 train. After that chat, our driver announced that the next train out is actually the one on Platform 2. (I think our driver didn't know which train was leaving first until after the chat).
So everyone got off the Platform 1 train and moved to the Platform 2 train. No confused "tourists" remaining onboard the Platform 1 train - it became completely empty. Everyone seemed familiar with the process.
Interestingly, the train on Platform 2 was listed as an "Edgware Road" train by the station describer, but was actually a city train on the train describer! (Can't remember exact destination)
In summary, both the destination and first departing train of the Wimbledon station describers are wrong. I think it would be better to switch off the station describers, and let passengers see the destination on the train describer.
I checked the Trackser app at Southfields and matched the train numbers. It corresponded to the station describers at Wimbledon, which meant it was wrong as the two trains discussed above had their destinations swapped on the station describers.
At Southfields itself, the station describers showed the destination as "District Line", which was good.