Post-upheaval. Purah explains that it and all of the Skyview Towers were all created post-upheaval with the express purpose of searching for Link and Zelda after they went missing. Considering that and all of the environmental changes being described as happening post-upheaval as well, save for Death Mountain cooling off which is described to have happened a few years ago, the Upheaval is implied to be weeks or even a few months old. Plenty of time for the ol' Hudson Hustle to set up all that stuff. When you think about it, that also means Link was incapacitated for quite a while, huh? It's got nothing on his previous hundred-year nap, but still.