I've seen the dangerously misinformed try to use wood to soften the blow so as to not "beat" the shaft/prop. That's actually the best way to actually bend something and is done by those who think they know what experts are. You have a taper that by design creates a greater surface area so the microscopic pores of the metal can actually interlock. With a fully functioning taper you don't actually need a shaft key way or for that matter even the shaft nuts. It's just like the chuck on a drill press, nothing but the taper holds it on. Everything else is backup.
So, as I said, it's normal that a prop does not come off with just the puller tension. If it does, what it really means is that your taper is not doing the job it should and that you will need to do some fitting. The goal is not to beat the prop off. The goal is to create a ringing shock wave that will cause the metal to vibrate and allow those intertwined metal pores to move. The puller simply creates pressure so once those intertwined metal surfaces start to move, that they don't settle back together. Right at that moment, the prop pops.