This game is fun but the marketing that it is "real time" seems completely false and unnecessarily confusing. So for anyone else who thinks their game is bugged: Despite the game showing you a real-life clock time and real-life day of the week, the in-universe time of the game itself is not actually pegged to real-time at all and things seem to just progress a bit whenever you open the app. Still fun but I think the devs should stop using the phrase "real-time" in the description since it's simply not true.
Glad you're enjoying it! While it's not 1:1 with real life due to design constraints (we wouldn't want to force people to play at certain times of day to progress, for example), the story does progress in real-time and text messages are sent according to the system clock. The game takes around 1 full month of real world time to complete in a typical playthrough (although some may finish it a little faster if playing very often).
I see. I would really suggest making this more clear in the description (and maybe in the game itself). The use of "real-time" plus the in-game clock and weather/calendar app being sync'd to reality and not to the in-universe time really makes the fact that it's not 1:1 feel like a bug instead of the intended experience.
I don't find this to be a huge deal but just to add to this, here's the part I just went through:
"ill be over real soon, okay?"
"okay, thanks tomoko"
"im here!"
"got home safe!"
Those messages came in one after the other with no delay. So to bdorfman's point, that felt like it might be a bug? Again I don't really mind, just want to make sure things are working the way you expect!