I think I may have the answer, albeit it is a long shot.
First, I'm going to guess the AI was advent, and had Destras. With the passive buff Destra's deal 1.5dps over time (iirc). Also, should you have whichever of the capital ships with the domination ability, you could have captured a Destra. I've heard that sometimes the buffs/debuffs are not properly rewritten when ships are captured with domination, as such it may have captured a Destra, but even though you had the Destra you still were affected by the passive damage buff despite it being your own ship.
If this isn't the case, then I haven't the faintest idea.