Developer Sarina DuPont from Embarcadero has a tutorial up explaining how to use the pull to refresh functionality of a TListView in Delphi XE7 Firemonkey. In addition to the pull to refresh functionality it also demonstrates how to update local data using remote data via the BaaS components. The pull to refresh functionality is enabled by setting the PullToRefresh property to True in a TListView. This allows you to drag your finger down the list on Android and IOS which will fire the OnPullRefresh event. In the tutorial it shows how to call the BaaS service Execute procedure to update the data contained in the list from the OnPullRefresh event. The data from the BaaS is linked via LiveBindings to the TListView and you can use either Kinvey, App42, or Parse for your BaaS backend. There is very little code that actually has to be written because most of it is configured and set up in the various components that are linked together via LiveBindings.
Head over and check out the full blog post tutorial about using the built in Pull To Refresh functionality in the Delphi XE7 Firemonkey TListView control.