By default, the sync with your Facebook page is off.
In order to turn it on, simply check the Facebook sync checkbox on the menu in Settings section:
Please note that we currently support sync only for posts with photos or videos, posts of other kinds e.g. text only or links without big preview photo won't sync to the App.
The sync of posts from your page to your App is made every round hour, unless you enter the admin App, it triggers a sync.