Since issues can arise from multiple sources, when setting up integrated security on an SQL server data source, we detailed a couple of steps to help out and diagnose the source.
- In Remote Desktop Manager go to Help – Application Logs – Report (tab). 
- Click Delete All. 
- In File – Settings – Advanced: 
- Raise the Debug level to 1. 
- Uncheck Disable stack trace. 
- Click OK.  
- Reproduce the issue. 
- Once the issue is reproduced, go to Help – Application Logs – Report (tab). 
- Click Send to Support. 
- If you already have an ongoing ticket with us, please specify the ticket number in the Subject. 
To learn more on contained database, see Microsoft's Contained database – SQL Server
Run the following script to find out if your database is contained.
Make sure to replace rdm-database-name with your Remote Desktop Manager database name.
SELECT name, containment, containment_desc, compatibility_level FROM sys.databases WHERE name = 'rdm-database-name';
If you execute the statements manually in SSMS (SQL Server Management Studio) what do you get?