"Forced Requisition" can miss the timing for its initial activation (flipping it from face-down to face-up), but that's all. Once active, it will trigger for any and all discards, regardless of whether it was a discard via cost or effect.
Some common methods of initially activating "Forced Requisition" include "Graceful Charity", "Dark World Lightning", and discarding at the End Phase when you have 7 or more cards in your hand.