[whpalmer4]

The desktop app automatically syncs at startup, one minute after you make a change, hourly thereafter, and when you quit. These intervals are adjustable via the Terminal if necessary, but for most people there should be no need to do so.

The iPhone/iPod Touch app has a setting called Auto-Sync which controls whether or not the corresponding behavior is active. With Auto-Sync on, you get a sync at startup, a minute after a change, and hourly thereafter if you leave the app running (no sync on quit). With Auto-Sync off, the only syncs that take place are when you tap the Sync button.

There is no way to get live database updates to the iPhone/iPod Touch if the OmniFocus app is not running.