Analyst MSDB Access SQL Server 2017
There are several things that could cause SSMS to attempt to connect to a certain database at logon:


If the user is in an AD group, and the login for that group has the msdb database set as the default.  If the user belongs to multiple groups that have logins, I don't know which login it uses to decide which database to connect to, but nonetheless it will use one of them.
On the connection dialog in SSMS, click the options button and note that the database to connect to can be specified.  This setting is persistent, so if it was set to msdb in the past, it stay that way for the user until changed.
On the connection dialog in SSMS, click the options button and select the Additional Connection Parameters tab.  This setting is also persistent, and if "database=msdb" was specified there at some point, removing it will resolve the issue.