This site allows you to run a script to test how anonymous you are.

http://ip-check.info/

One of the things is tests is named "HTTP session" and moving the mouse cursor over the "bad" rating it explains that:

"Your Internet or VPN/Proxy provider may link each of your HTTP requests with earlier requests. He may thereby trace you perfectly. Your Identity is not protected. JonDonym protects against this attack"

I do not understand how JonDonym "protects against this attack". Can the sites you visit through JonDonym trace you or not? It is the sites we want anonymity from, not the provider of anonymity. The provider is trusted, is he not?

Not: cookies and scripts completely disabled.

I doubt most ISPs have the capacity to track every connection of every customer 24x7, this would require inspection of every single packet passing through which means big $ for big equipment that provides no financial benefit to them. They could perform tracking/packet inspection for a specific case if requested by law enforcement though.

If onion routing (or equivalent) isn't used, then yes, the VPN/Proxy service provider will know what sites you're visiting. In fact, if the sites you're visiting don't use end-to-end encryption, the provider will be able to see all your communication with the site too. I don't know how JonDonym does things. Why not simply use Tor and some appropriate Firefox extensions? Is it due to performance reasons?

I mean, Tor is specially designed for this sort of thing.

Tor is too slow. This claim by JonDonym is strange, it is like saying

"At JonDonym we are blinding ourselves so we cannot see a complete list of sites you are visiting but only one site"

And if so how does the testing site know whether JonDonym are blinding themselves or not?

Well, I'll admit after a quick glance at their site it seemed like a scam to me. That was just my initial impression, though. Perhaps they do have some sort of onion-like system in place where you get some of the benefits of Tor without the performance issues. I really don't know. Have you considered asking them directly? That is, assuming the information isn't available on their website.