I looked into it enough that I can explain it. There are four things involved here:
- The visual positions, which are the only thing the player sees but which the game doesn't care about,
- Switches, which say if the statue is in a solved state,
- Variables, which track how many times the statues have been turned so the game can set the switches and self switches and, for most statues, reset the variable itself when it gets high enough,
- and Self Switches, which when set normally only reset the corresponding switch the next time the statue's turned and then unset themselves.
The reset button only resets the statues' visual positions and variables, which means the game thinks any that were in a solved state still are. For the statues that need two turns to solve, this isn't a problem. For statues that need one turn to solve, the self-switch function is activated after the switch is activated, so you'll need to turn it a full revolution to get it into a solved state.
For the statues that need three turns to solve, however, the self-switch is also used to reset the variable. This means that pushing the button while those statues are solved causes them to end up offset by one until they're reset while in an unsolved state.
So if the statue puzzle gets bugged, then hit the reset button, turn every statue until it's in neither its starting position or the solving one, then hit the button again to properly reset them.
...Or if you were asking what bugs it in the first place, then the answer is that leaving the room and re-entering only resets the visual positions, and trying to use the reset button causes the problems I just explained.