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It should sync 1 minute after you make a change, and hourly thereafter. I think it will also sync on launch if it has been more than an hour since the last sync, but my kid won't surrender the iPad to allow me to confirm that :)

If you want to be sure that any changes you've made are "flushed out" to the sync server, then sure, tap the sync button and wait for the wheel to stop spinning before closing the app.