we played last night using the slot machine and the neutral(white) variant. Sounds like you played correctly. The White neutral dice are treated like an imaginary player, so they compete for the bank notes like the other players in the same way. Any bank notes that the White dice win, or that are not won, are placed at the bottom of the bank note pile (or deck).
Someone played one dice of their own and one white dice on the slot machine. They didn't play any other dice so in the tie breaker neither the player nor the dummy player won on any of the tie breaks - each having exactly one dice with the same value. What should we do in this situation?
I could see arguments for either the player always beating the neutral player or the neutral player always winning or neither winning.
We just played that no one got any banknotes as they hadn't 'won'