The Tournament screen updates once per second, at which time every item on the screen is checked for changes and updated if necessary. If anything changes (which it will have if you have the clock, or current time of day, or elapsed time, etc, etc, displayed), then IE (the TD runs inside of Internet Explorer) has to re-evaluate the underlying HTML code and re-render the screen. This, unfortunately, is not necessarily "instant". And it will definitely depend on your PC's speed.
Honestly, on the PC I am currently using, which is fairly beefy, I don't really notice a stutter. But there are plenty of other PCs I've used where the stutter was quite noticeable.