Force Contacts update in iOS9
In Settings, visit "Mail, Contacts Calendars." Scroll down and select "Fetch New Data." Then, on that screen, temporarily turn on "Push," and then make sure iCloud is also set to push, so that new data is pushed from the server automatically whenever possible. This should push through any new data immediately. 

You may then want to switch Push off for data, and choose one of the Fetch settings to save battery.