No app should work, but this was a very minor update, only a few minor code changes ahead of the release coming in a week or so.
All updates for this chapter are "free" after you pay, i dont reset payments like some devs do.
the only question is when the chapter change happens, originally slotted for day 10, its could likely happen at day 5 due to mobile size restrictions. But if it happens at day 5, then chapter 2 will also be free if you purchased this, as I feel $10 for 10 days is a good distribution.