It looks like they are using Coinfirm API to get information about a particular Bitcoin address. They make a request to a specific Coinfirm API endpoint, retrieve data from the database, parse the received data, and then make a decision to accept or decline the address in a CoinJoin transaction.

Here is an example of Coinfirm API: https://app.swaggerhub.com/apis/Coinfirm-swagger/API/3.0.9#/Transaction%20report/get_transaction_report_reports

Of course, in order to try it out, you need to create an account with Coinfirm.