You can trigger the API call when you navigate back to the first page like this pseudo-code
class PageOne extends StatefulWidget {
  @override
  _PageOneState createState() => new _PageOneState();
}
class _PageOneState extends State<PageOne> {
  _getRequests()async{
  }
  @override
  Widget build(BuildContext context) {
    return new Scaffold(
      body: new Center(
        child: new RaisedButton(onPressed: ()=>
        Navigator.of(context).push(new MaterialPageRoute(builder: (_)=>new PageTwo()),)
        .then((val)=>val?_getRequests():null),
      ),
    ));
  }
}
class PageTwo extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    //somewhere
    Navigator.pop(context,true);
  }
}
Or you can just use a stream if the API is frequently updated, the new data will be automatically updated inside your ListView
For example with firebase we can do this 
stream: FirebaseDatabase.instance.reference().child(
      "profiles").onValue
And anytime you change something in the database (from edit profile page for example), it will reflect on your profile page. In this case, this is only possible because I am using onValue which will keep listening for any changes and do the update on your behalf.