Will I be fined for overstaying my tourist visa if I can only extend it when the immigration office reopens?

If your stamp expires on a day the immigration office is closed (weekends or holidays) and you go the next day they're open to get an extension you will not be fined for the overstay but you will get the overstay stamp in your passport. It will have a "fine waived due to closure" stamp on it.

There is no down side to waiting until a stamp expires to get an extension because they add the extension to the expiration of the current stamp. That means you don't lose any days going early.

I'd go there today.