Hello nickfromsingapore.
Welcome to Apple Support Communities.
If I'm understanding correctly, your iCloud contacts are syncing properly with your MacBook Pro, however they are not syncing with your iPhone. I will be glad to assist.
I would recommend checking the iCloud contacts settings on your iPhone.
Please see below from the following resource:
Keep your contacts up to date on all of your devices with iCloud
- Go to Settings > [your name] > iCloud.
- Turn on Contacts.
- When you're asked if you want to Merge or Cancel, tap Merge.
All of the information stored in Contacts uploads to iCloud."
Then review the information in the following article:
If your iCloud Contacts, Calendars, or Reminders won’t sync
Cheers.