The purpose of iCloud Sync is to sync preferences and account between iOS and Mac OS X devices.
With airmail app you have control over what settings can be synced.
If you have problems with iCloud sync, please read the troubleshooting guide here.
Edit iCloud Preferences
1. Tap the menu icon ≡ in the top left corner on the app, which will reveal the menu.
2. Tap on Settings
3. Scroll down to iCloud Sync and tap on it.
You can switch off iCloud sync or set it as 'Import only' by tapping on an account and enable/disable common features as shown below.