Haystack has a number of 'sync' options. If you are looking to 'sync' your Haystack contacts into your phone, please view this article for iOS, or this one for Android instead.
This article is about the sync in the opposite direction (sync contacts from your phone into Haystack).
When you choose to use the "search my phone's contacts" feature in the app's settings, Haystack searches your phone's contacts to find which of your phone contacts are on Haystack.
For maintaining privacy, Haystack only imports your phone contacts which we already have in our database, and we have additional information to add to your phone contacts. So only relevant contacts will be added to your Haystack.