I didn't play it much, but it took any altering of time as a form of time travel. The 3ds didn't have a built in time savings system so you had to go back and manually change it. Or so I did anyway (if there was). I got Tomadchi Life around the time daylight savings was ending or beginning and had to go back/forth an hour.
So for an entire week if you time traveled or had to adjust the clock to get the right time, the game punished you. Like it didn't even matter if it wasn't by a full day and you just changed it to a minute/second. The game had these special events that would take place and skits/scenes that happened every hour or so at the fountain plaza. So adjusting the clock in any form made it where nothing happened for an entire week. Like it was so hardcore punishment I don't know why there weren't more people being vocal about it. It wasn't even worth playing the game for that week because nothing happened at all.
And I never have heard anyone complain about it. Or even bring it up. During the punishment time, if you adjusted the clock in anyway again, it went back to a week sentence. I learned that the hard way when I realized my NL time wasn't right and had to readjust it.
Kind of brings back memories of Smash4's Smash Purgatory(Hell) and for those who don't know, it was a system that punished everyone equally and threw them in a banned server. But they didn't know because they were never told that they were punished/banned and for what reason. I got it for 2 weeks or so and to this day don't know who reported me because I never do anything mean spirited. You could simply report someone for playing a character you don't personally like and it would be filed as a legitimate report because the online system was so poor.
Which is how Tomadachi Life handled altering the time. It never told you why. You just kind of figured out when nothing was happening.