Full disclosure
You don't have a lot within systems like these: much of what you do can be monitored.
The applets in the web pages run within a 'security sandbox' which means they do not have any general access to your machine itself (to your files, data, etc.) However, the applets themselves can certainly 'call home' . A typical useful application of this is in a class setting when students are trying to submit the results of a quiz or exam. A suitable Deriver applet can send these results to a database for the students. One assurance about Deriver and privacy: it will never call home invisibly-- it will tell you what information it has sent and why.
Of course, once you start using networked computers you have no privacy anyway (to paraphrase Scott McNealy, of Sun, 'you have no privacy, get over it').
You may or may not know this but your networked computer is calling many homes all the time (checking for software updates, reporting which web pages you have visited and the advertisements you have clicked on, etc.). And that discrete communication activity is nothing to do with learning logic and these web pages.