The Other Contacts is a secondary contact agenda to your mobile device, so you can store the contacts you need to differentiate them from the ones you have in your main agenda.
When you create a new contact, the data of this is stored locally on your device so that if you do not have a connection you can see the contact information of that person. Also, when you create a new contact it is synchronized with iCloud (service of Apple Inc.) so that you never lose the contacts that you have stored in the app even if you change your phone. (You can read the privacy policy of iCloud in: https://support.apple.com/en-en/HT202303)
The application never shares the data that you have stored in it with any third party, nor are they visible by the development team. Either way, you always have the option in the settings of the application to completely delete all data stored both locally and in the cloud.
Regarding the QuickContact function, which generates a QR code of your own contact stored in the application so that anyone else who can scan that code can add your contact data quickly, stores the information related to your contact only and exclusively locally. This means that when you change your device you will have to reassign in the application which contact you want to associate with QuickContact since this information is not stored in the cloud nor does it use any third-party service to generate the QR code.
In relation to third-party services used by the application, The Other Contacts uses CloudKit as a means of storing data in the cloud.