Required: Contacts App for iPhone 5c (IFTTT Compatible)
The IFTTT recipe gets information from a specific source (channel) that is defined in the recipe. In this case I assume that you use a recipe which imports contacts to a spreadsheet on Google Drive and then it only imports contacts from the contacts application (the built-in one).

From what I am aware of there isn't any application currently that offers this synchronisation with Google Drive via IFTTT other than the iOS built-in one.