Need some clarification on user management in Salesforce?

We have created one system administrator user. We apply some duplicate rules on Account page.

When we update the account address using third party app, it is working fine.

Now I created one user under my system administrator account. Now that created user when going to update the account address using that third party app, it is not working.

Please any help out on it. We know problem is duplicate rules of Account. How can our third party app ignore this duplicate rules?