> We're not invoicing in advance of fulfillment
It is definitely not the most clear, but probably the reason NS phrases it that way is because the behavior you observed (invoicing everything on the SO) is NS's standard behavior until you change settings, use subscription billing, billing schedules, etc.
Shutting off that Invoice in Advance of Fulfillment should make it behave like you want in that clicking invoice will only invoice the fulfilled item though you might have to shut off that other flag too. I'm less familiar with that.