We have an SSIS Server and a Database server. SSIS Package unable to connecting to remote SQL Server while running the package, however, it works fine when someone is logged into the server.

Extended events shows the error 10054. Most of the troubleshooting taken into consideration as per the MS article

Why this is working when someone from the DBA team has a RDP session.

Also, Firewall logs shows traffic against RDP user instead of SSIS Caller account which runs the package. Network team told there is no traffic from the user.