I know how I respond to “or else” threats.
That makes two of us. I consider a threat as an attempt and deal with it...on the spot.
In that case they are leaving up to you to decide what the “or else” is. And you are then take appropriate action based on your own understanding.
From the other side, the best threat is the one that leaves it up to the imagination of the receiver as to what it means. The receiver will imagine the scenario that they are least capable of dealing with. It is bullying at its best.