Ah, I love slinkies.
I'm going to try to give a more general (if more complicated) answer to this question. It's really all a case of relativity. There's no difference between a person falling to the floor and the floor rising to a person. The only difference between those two situations is the frame of reference; whether you're observing the situation as the floor or the person. This gets complicated at high speeds, because light is weird, but a low speeds it's not that bad. In any situation with regard to UA and the Equivalence Principle, remember relativity. The solution may not be quite as intuitive as you hope, but if you think about it there will be a solution.
So in this particular situation, we need to look at what is happening from the UA frame of reference. The bottom of the slinky is being accelerated at 9.81 m/s2. So is the top, starting off. But then the top stops accelerating, as it is no longer attached to anything. Now the bottom is going to stop accelerating, but it takes it a second. As for why, imagine the reverse. Hold a slinky still and then suddenly pull it up. It's going to stretch, because the bottom doesn't automatically change speed when the top does. It's the same principle.