Currently native iOS and Android apps have baked-in support for pull-to-refresh. This means when you drag to scroll a page down past its top edge, a spinner appears. If you scroll down low enough and then release your drag, an event will be triggered, allowing you to e.g. fetch new data.
Using it is very simple: simply drag in a Receive event node, set the Event source property to Page refresh, and connect some logic to it.
Once you have the event node on the page canvas with some attached logic, Composer will automatically enable pull-to-refresh functionality for that page.
At the moment, the spinner spins for a set amount of time and you can't configure how it looks.