You only get one free tag on an aspect. If it's fragile, the aspect goes away once it is tagged. If it's sticky, all subsequent invokes require a Fate Point.
So, if the demon has a 'missing arm' and the Knight passes the tag to anyone, the next person can tag it for free. The demon does not receive a FP.
Anyone else afterwards must spend a FP to invoke it again and that FP gets paid to the demon.
It's the same with any aspect. If someone does an Investigation Assessment to discover a scene aspect, only that person gets the tag...unless they choose to share the tag.