Contact Syncing automatically makes all Haystack cards and contacts available in the iOS contacts app.
Any changes made to a Haystack card will instantly update in your iOS contacts.
To turn on Contact Syncing, toggle the Contact Syncing option in Haystack Settings.
PS. Contact syncing only syncs your Haystack contacts "TO" your iPhone. Haystack does NOT "read" or "transfer" any of your contacts data from your iPhone to Haystack.