I have a Varia RTL510 (software version 3.50) radar paired with an Edge 25 (software version 3.30) bike computer. When the bike computer is turned off and I plug in the charging cable, the radar turns itself on a few seconds later. This seems like a firmware defect. I know the radar is supposed to automatically turn on when the bike computer turns on, but it doesn't make any sense to do that when connected to the charger. So then I have to manually turn the radar off every time I charge my bike computer.
You need to turn the Edge off whilst its charging rather than turning off the Varia. Edge usually turns itself on when you plug it in and this switches the varia on. If the Varia didn't turn on when the edge was charging and switched on the charging on the move wouldn't be possible.
The problem is why the Edge units all turn themselves on whenever a cable is connecting rather than just staying on if already on or staying off when already off, which would be the sensible solution
Not sure if the Edge 25 has the following option, but on some units under Light Network -> Network options there is an option labeled "Light beam activation" , this can be set to Timer start or Device Power up.