Ellie's husband, Mark, works at the State Department as we find out right at the beginning of the film (so it's easy to miss). I think it's safe to assume that when she hears the dinosaurs and Dr. Grant's cries for help on the phone that she contacts him and explains the circumstances. He then probably gets the wheels in motion to send a rescue team to Dr. Grant.
ELLIE (CONT'D): So, Mark's working at the State Department now.
GRANT: Really? (To Mark) What do you do there?
MARK: (with mock bravado) I could tell you about it, but then I'd have to kill you.
It's fairly safe to say that given this exchange he's fairly connected and can definitely get the message to the right people.
http://www.imsdb.com/scripts/Jurassic-Park-III.html (Scene 5)