Say I have an attack which causes damage and vulnerability on hit, until the end of my next turn. (for example Psion's Mind Break). Does the damage from the attack causing vulnerability deal extra damage, assuming the opponent was unafflicted by vulnerability previously?
The Rules Compendium on page 92 says "Sequence: The order of entries in a power description is a general guide to the sequence in which the power's effects occur."
So as Mind Break says: "Hit: 1d8 + Intelligence modifier psychic damage, and the target gains vulnerability to psychic damage equal to your Charisma modifier until the end of your next turn.", the vulnerability to psychic damage is applied after the psychic damage. Note that the effect lasts until the END of your next turn, so it would apply if you use the same power again next turn.