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[Gigantus]

Did that testing by using this simple script in Bare Geomod:

    monitor_event PostBattle CharacterIsLocal
         and Routs
        historic_event FIRST_WINDMILL
    end_monitor

First stage was to test the triggering without the Routs condition: the message fired in autoresolve, regular end of battle and forced exiting.
Second stage was to rout a unit and then conclude with a forced exit: only the commanding officer triggered the script and only if he had exited the map completely. A simple exit from the battle (pic gone from line up) was not sufficient - the green pip had to leave the radar map completely. This can presumably be used as a minor exploit to preserve the general of an annihilated\totally routed army from picking up that trait: the battle will stop if he is the last unit over the battle line, but will not count as routed as he did not exit the map completely (requires testing).

Summary:
Forced withdrawal\routing (clicking that button) triggers the condition
but only for the commanding unit (very likely for other named characters as well - not tested)
and only if it has left the map completely

Which means that the claim of regular units being withdrawn was the reason for obtaining the negative trait is not valid.
Not valid as well is my assumption that the condition would fire for any unit within an army.

Which means the exploit of expending a missile unit's projectiles and then withdraw it completely for protection (or replacement) will live on, or whittling down a unit to minimum numbers and then force withdrawing it so that fresh re-reinforcements can replace it. But then it's a prerogative of every player whether he really needs to perform actions that are not available to the AI, so let me not harp on about it.