It should be continuous not just on the cast. However, Some of these mechanics are based off of Net Fury gained and lossed.
basically if you cast a spell that costs 30 fury, but in the process of casting the spell you generate 30 fury, the mechanic reads that as a net fury spent of 0. You actually have to see the fury bar go down for it to register as fury spent.
this is true for some of the cool down reduction on fury spent mechanics (i.e immortal king set bonus, or the now defunct thrive on chaos rune for WOTB) I don't know if it's true on life on fury spent.