There is a "highscores light" page provided by Jagex that the program automatically sends a request to once per day for each player added to Clan Stats. It's a simple matter to sort the data out and store it in a database, which Clan Stats uses to display the info in meaningful ways.

Here is a link to the RuneScape Knowledge Base Article that talks about it and below is a link to the highscores light page, if no RuneScape name is given at the end of the link enter yours and if you have spaces change them to underscores '_' to see your highscores light page:
http://hiscore.runescape.com/index_lite.ws?player=

As explained above Jagex provides a special page to allow programs to view skill data for players. Clan Stats grabs the same data that most calculators and forum signature makers on other fan sites use. It's essentially a fancy calculator.

Clan stats does not directly interact with the in game functions in any way. The data shown here is for informational purposes only.

This site is created and operated solely by NESGamepro, feel free to add me in game, my public chat is usually on. I am a hobbyist web programmer and I do this for fun. This site is my baby and I enjoy working on it and talking to like-minded stats junkies and RuneScape fans. There are no ads because I pay for it all out of pocket rather than clutter the site up with slow loading junk. It really is as simple as that, all I ask is that you enjoy it or tell me what would make it better.

Yes, you only need to exit to the lobby for your RuneScape highscores to be updated, you don't need to log out fully. Clan Stats will then see the changes during it's normal data update time.