Your problem is that the site is being cached.
The question is "Where?" There are a number of places between your computer and the website’s server.
Firefox is pretty good at not caching a site (shift + refresh will clear a cache, anyway).
If it’s not that, it’s probably your internet provider. Your only real solution (that I know) is to set up your computer’s DNS to go through OpenDNS. (There’s a free version.)
It’s awesome, but can act weird for odd non-normal internet connections…