If they are saying they are seeing the wrong login screen, you can test that by entering the organization ID and seeing where it sends you. You should be able to tell the difference between their SSO or the qualtrics login screen (it will show the url at the top too).
If you want to test that logging in is redirecting them back to the app authenticated (without a pop-up), you will need credentials on their SSO. Often times they can create a test account with only access to this application.
The only other way to test would be to use your own test SSO service. OKTA for example has free trials. This could help you make sure your configuration is right but if it works, it's not going to help you troubleshoot this issue.