I always do it for WDW on my iPad using the Safari browser. One time, I had read a lot of posts saying Safari wouldn't work, so I downloaded both Firefox and Chrome. I couldn't get either to work and used Safari, which worked just fine.
I think what works depends on a combination of device and updates to the operating system, browser app and Disney's app.
It works fine from start to finish for me on an iPad - that's how I've done it each time.
The Safari web browser app on an iPhone is pretty much the same as on an iPad, so if you start on the Disney website
DAS page on your browser, I'm not sure why it would work the same as on the iPad