When a fire is put out by throwing a splash water bottle, it won't cause updates to BUD systems. I am not sure if this is intended behaviour or not.
What I expected to happen was it would cause an update, similar to if the fire was put out by a player.
1. Build a standard BUD using a upward facing sticky piston with a slime block on top and then a redstone block
2. Place netherrack below and to the side of the BUD so that the fire lit would be next to the Budded piston
3. Light netherrack on fire
4. Put it out (to simulate player putting out fire)
5. Then try putting the fire out with splash water bottle. (This will not cause the BUD to fire)