How iCloud sync works
iCloud sync is optional. A new install keeps everything on the device, and you turn sync on in Settings if you want it. If you already had sync on, it stays on.
When it is on, your contacts, notes and selfie photos sync through your own iCloud account. They are never stored on Common Nexus servers, whether sync is on or off.
Backup
ShareCards and reminders do not sync between devices. They are included in your backup: open the … menu at the top right of your wall, tap Settings, scroll to Backup & Restore, and choose Export My People. Restoring on the new phone brings them across.
If this page doesn't answer it, email support@commonnexus.com. A person reads it.