Hi Steven,
Your question is a bit unclear. Are you talking about an applet on a web page when you refer to "a timer in my website"? You should be able to pass an applet a value and have it run off that, rather than make it dependant on the viewer's system clock. However, no matter where you get your time value from, it's going to be dependant on the computer it's getting it from, which will be either the server or maybe the client machine in some applications, but not likely.
If you're just talking about a server-side script, then the time value is dependant on your computer clock. If you're worried about this being inaccurate, you can get software to keep your clock up to date with a master atomic clock. That's what a lot of commerical/production servers do.
Cheers,
Omega Wombat
http://www.drinknation.com