Android - My Phone Time-Travelled Again. How? and Why?

I thought I was the only one facing this issue, and I didn't even know how to describe my problem back then. Looks like we're on the same boat. Even I'm using the Moto G (XT1033), but on NXROM 10.2, and I started facing this issue around a year ago until last December. The phone randomly reboots when I'm using it, and as you had described, it went back in time, and all the messages, downloaded files, statictics for a period of time and other stuff just vanished. I tried to Google this up, and here is my understanding (I may be wrong, so please correct me if so):

It turns out that this happens due to a kernel panic, and when the fsync function is not executed. fsync is responsible for writing the data from the buffers (all changes you make to data, like new messages, photos etc. is stored temporarily here) to the internal storage. When a kernel panic occurs, all the data in the buffer is not moved to the internal storage, but just vanishes. So all those changes you made just vanishes into thin air.

I was pretty frustrated about this, and then I stumbled upon LSpeed (available on Play Store). There was a battery profile which emphasises on conserving battery life. It disables kernel panic, and modifies a whole lot of other settings. Since I installed that, I've not faced this issue again. Try this out and do let me know how it works out for you.