it should be noted that you should not have won immediately, as the damage card you pulled should have gone into your command line. So you should have rolled the 6-sided die, put the card into whatever numbered space was rolled, and then next turn when you were executing your command line, if you can still use the card to tow the bomb, then victory is yours!
Only the cards with the trash can icon happen immediately, the ones with the slot icon don't happen immediately but instead are put randomly (usually) into your command line.
You always execute a damage card's effect before discarding it/putting it aside the command board/rolling a die and putting the damage card in a slot.
It's on the rulebook, under "Damage".
For all damage types, first execute the instructions on the DEAL Damage Card.