my daughter used someone else's cell phone, although she took hers- probably run out of battery as usual.. dizzy kid! I sent her with tons of phone cards as well (to share she said!) just in case too :)
The "I'm here!" call is made from a cell phone. There are no phone banks in In-processing. Calls after that require a phone card, which they will get in thier ditty bags and can also buy at the NEX--it's good to have an activated one or the free ones from callsforrecruits.org though. See Arrival and What Happens at the RTC and Phone Cards and Phone Calls.