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Do / prevent X unless Y

 When do you pay the cost of Y in cases like:
 Vodalian Mage
 Lim Duls Hex
 Soul Barrier
 Presumably as part of the resolution of the appropriate effect?
 Is this still true where the X is damage and the Y is damage 
 Presumably if the source is destroyed after X, but before Y then
 you can still pay Y (eg Naf's Asp destroyed after it damages. It
 could still do extra damage and extra damage could still be prevented
 by paying 1 mana)
 Prevent X unless you do/pay Y: timing slightly different?
 eg Brainwash. Do you have to pay the 3 mana before assigning the
 attacker, after assignment, or as a cost to assign?
 eg Drought. Is the sacrifice done before anouncement, after or 
 as an additional cost during anouncement?