The stop button does work. It does what it is supposed to do. It isn't there to stop a spin, it's there to stop multiple spins.
Wheel of fortune prizes are awarded the second you hit apply. You see it on the odd occasion you get cents. They get added to your tally as soon as the spin begins.

Save your daily amulets for 3 days, when you start an apply, change the 1 to 3. Hit stop. It will only use 1 amulet, not 3.