I do not understand why you having issues with the link you provided. It is quite clear.
SSIS Package (call it myfile.DTSX) - you create a connection manager to your database - Name it MasterSQL and set it to "Data Source=myserver;User ID=myuser;Initial Catalog=mydb;Password=mypassword"
now on your command line you wish to change this connection string to point to another server - and using a different user
your command line (in package deployment mode) becomes
dtexec /F myfile.dtsx /Conn "MasterSQL";"Data Source=MyProductionServer;User ID=PRODUSER;Initial Catalog=master;Password=PRODPassword"
you could also do it using a variable instead.
same SSIS package.
create variable type string - name it mydbconnstr and set it to set it to "Data Source=myserver;User ID=myuser;Initial Catalog=mydb;Password=mypassword"
on the properties tab of the connection you have a expressions line - by selecting the "..." on it you get a pop-up where you can assign particular properties of to variables.
select the one named "connectionstring" and assign the variable you created to it.
your command line now becomes
dtexec /F myfile.dtsx /SET "\\package.variables[mydbconnstr].Value";"Data Source=MyProductionServer;User ID=PRODUSER;Initial Catalog=master;Password=PRODPassword"
note that in either case you may need to escape the ";" and the quotes - again the link you supplied show how to do it.