Most cloud storage services are encrypted and only you can access them. The content is encrypted, and the encryption key is also encrypted. The key used to decrypt the content is generated based on your password which means you are the only one who has access to files and contacts.
This means you should be safe as long as you use an account-based cloud storage service. For example, Google Drive, Dropbox, and OneDrive can be used for such operations. However, try contacting those where you have the contacts backed up and they should provide additional information.