From your posting, you may have things a little backwards. If I go to new name, "www.savewater.co.nr", I see a Website Wizard Layout that simply says "We Have Relocated! Visit Us now at www.savewater.co.nr". But that's were I thought I went.
If I go to the old name, "www.savewater.tk", I see a Website Wizard Theme with about six pages. That means that they both published. Not being able to see your changes, or published outputs, right away is usually caused by your browser cache. When you make adjustments like that, you need to clear your cache and force a couple of browser refreshes (F5 or Ctrl-R).
However, it doesn't sound like they are in the order that you want.
I don't think it's a browser issue or a "publishing" issue. Publishing is nothing more than the act of uploading your files to your web site. There is no such thing as a 30 minute publishing delay. However, the ".tk" and ".co.uk" "free" domain names are usually rather slow and not very reliable. I have tried them all before and haven't found them very useful. It can take a little time for changes to get through their systems.
Hey Martin, we do have computers on this side of the Atlantic. The only difference between .co.uk and .com is a couple of thousand miles of ocean with some high capacity telecoms cables underneath it.