If you launch a program that should access the internet, and it then does access the internet I wouldn't take this as suspicious activity. Particularly so if the sites are known to you or at least not questionable.
I don't have an explanation for the particular connections Trillian and iTunes are making but I do have a guess. Since Trillian functions with multiple chat services it probably looks at your connections to see if you're connecting to one of the supported servers. Similar for iTunes and internet radio, etc. As I said, this is a guess and others may have better insight on this.
On the other hand, if you see programs seeking internet access when you haven't run the program (other than background processes like Windows Updates), programs you don't recognize, or access to sites in China, Russia, etc you should probably investigate further.