The "minimum interval" settings specifies the minimum time between automatic syncs. The actual time between auto syncs is determined by iOS and is typically 1-4 hours but it may take longer depending on a number of factors including whether you're connected to wi-fi, whether your phone is plugged in, how fully charged the battery is, and how often you use this app.
This help article relates to the iPhone app called "Contacts Sync" which can be downloaded here:
Need help? You can email us at email@example.com