Good question!
We've been doing the former. That +1 forward sits there, pregnant, waiting to be used. It's pretty cool, because it changes the social dynamic of the characters - and of the players! - when there's a dude who knows something about you that you just kinda let out of the bag unexpectedly and you know that if you play this right they could help you with it... but if you piss them off it could come back to bite you. It's delicious.
I do rule that spending the +1 forward to help/hinder must make sense within the context of play (i.e. the player has to argue how they are using the secret to help/hinder).
I should also point out that one of the reasons I think it's working so well in the current game I'm MC'ing is that we represent ongoing/forwards with physical objects. There's something deliciously meta about absently playing with a physical manifestation of another character's secret as the session unfolds. Good fun.