Hello,
Thank you so much for posting here.
"Although this application is configured to see users in the customer's domain perfectly fine, AD users from our domain show up in their user search results."
Sorry that we are not familiar with the third party application. What account will log on to this application? If we do not want this logged account to read the user information, we could try the below from the AD aspect.
Open the user OU, choose "properties" and then choose "security". Add the logged account or the groups who will log on to the application, and then set Read permission to Deny.
I am sure whether it works. We could kindly have a check. But as for this configuration, there will be some influences to our AD environment. For example, if the accounts log on to other service or application, they also do not have Read permission to the users within the OU.
Since it is about the third party application, we could also contact the vendor to check how to solve the issue. Thanks so much for your understanding and support.
For any question, please feel free to contact us.
Best regards,
Hannah Xiong