spoiler
Was Luthen in the imperial military or was he in a separatist militia in that flashback? I couldn’t tell.
Honestly one thing I found a bit interesting in Andor is it seemed to cast the CIS in a more positive light. Andor was in a pro-CIS insurgency, there are pro-separatist characters, even though they join up with the Rebellion which seems dominated by people who want to restore the Republic.
This is what is currently on his Wookieepedia page, too, for whatever it’s worth. That scene is in 18 BBY, so early days of the Empire.