It can take time for changes to automatically sync to your iPhone contacts.
You can force the app to sync by:
1. Go to your iPhone 'Settings'
2. Tap 'Mail, Contacts, Calendars'
3. Tap 'Haystack'
4. Toggle 'Account' from 'On' to 'Off'
5. Toggle 'Account' back to 'On'
All changes should update in your phone contacts.