I think the labeling is not applicable for all.
a) The white wire on the left in your picture should be labeled “incoming hot” for the left driver. And
b) In my case the connections are mirrored as well:
If you unsolder the wire to the right cup, you end up with these connections from the main cable where the red one in the middle is the right-hot-signal but while black is still common ground, it is on the other side of the board:
( If you’re interested on how I modded mine, have a look here: The lazy person's *reversible* DT880/600_Ohm balanced mod )