Important is the date on the device running server, so in this case raspberry I guess. The interface is just a javascript webpage, so reloading in browser restarts it, but the daemon running Repetier-Server is responsible for setting history date, so it uses the time you see in th ebolt menu regardless of what your windows pc says otherwise. There is also a reboot option in main menu when you use our pi image.
Note that the fact that you can see pi in your local network does not automatically mean it has also internet access. That is normally the case, but if you have some router firewall active you could prevent it from reaching timeserver port in internet or block all internet traffic. A internet timeserver is used to set time after a restart of the pi. If you login via ssh or in gener settings->terminal you can see and change the date with the "date" command.
