The question is, when playing through a direct connection via cable, are autosaves saved only on the server or on both computers?
I'll answer your question again.
it doesn't matter who creates
Saves are naturally stored with the person who has them enabled.
The main thing is that the parameter EveryDaySaver = 1 is set. Whoever has it enabled will have automatic saves.
Therefore,
Autosave mode was enabled.