I think the "set time" thing is just between them, nothing to do with the app specifically - but I do admit this chapter definitely made me think "...does he actually plan to explain much more about how this works?" more than once. 😅 Not a deal-breaker, to my mind, but I find it intriguing in a way that he's gone for such a big concept right out the gate and then - at least so far - left so much of the details on the level of "a wizard did it". (Whether or not the app is supposed to be actual "magic".)
The "us" would imply that Sleep Goddess also finds it hard to sleep, so maybe she's taking like a 20% cut of all the sleep he sells or something.