Updating your old game map will take a while the first time but if the map hasnt been explored in for example a mountain area..ie you just identified the edge of the mountains...and that area is large enough to support RNG caves they will spawn there if possible. Since you didnt explore much if you have built a lot then this is worth doing... but if you havent built or explored much... just update your game and enter your old seed and start afresh

Here's the info from the pinned FAQ post:

"Will new content be added to my world I currently are playing on?

New content such as tar pits, mountain caves and Mistlands in the future will not appear in areas that have been already generated. Areas are generated 300-500 meters from a player's location. "Exploremap" and "resetmap" has no effect."

So if i already explored a Mountain but i go to another Mountain there's a chance that it will have caves.

As long as you have not explored an area, which means that you have not gotten closer than roughly 500 meters by foot or ship, then the first time that you use your old map it will update those unexplored areas.

It means that it will take a little while longer to start that first time, but that is normal. Thus, you'll get the glory that are the caves, pits and so on as long as the areas are big enough.

So, go and... I was going to say that those mobs won't kill themselves, but then I remembered the loxes, fulings and undead among others. Thus, go and party on, don't let the mobs have all the fun!

Edit: As long as you are exploring the mountain for the first time, there's a chance for one or more caves. It's somewhat random, as long as the mountain is big enough then there's a chance.