I am pretty sure that SQL Prompt (at the moment) cannot colorize the tab based on the SQL login (Windows or SQL). That is, if you log in as "sa" or log in as "RedGate\SteveJones" you will get the same color scheme.
What you CAN do is colorize the status bar (the yellow bit near the bottom that has "Query executed successfully" and the server/instance you are connected to) and this can be colorized based on instance AND partially by user. I say partially as it can colorize based on a specific SQL Login or ALL Windows Logins. So if you log in as sa, you can highlight it in red (for example), but if your windows login is IN the sysadmin role, it will be yellow unless you mark that windows logins are red.
Downside to this is you need to set it up for each SQL instance and login individually. And if you are using SQL Aliases or SQL browser for some of the times you connect and sometimes you include the instance and port, it becomes more of a pain as you need to set it up for EACH of these. So you could have one for "admin" connecting as sa, "adminserver\admin" connecting as sa, "adminserver\admin, 4321" connecting as sa, plus 3 more for each sysadmin account you have on there. Then repeat for each SQL instance you have... Management on that becomes a huge pain in the behind. And to make it more fun - it is SSMS version specific. SO you get it set up on SSMS 17, then install SSMS 18, you have to put it in again. Thankfully you can export and import, but that is a pain to do if you have 5 different SSMS versions too.
BUT if you do want to go this route - click on view->Registered Servers. Then expand "Database Engine", right-click on "Local Server Groups", select "New Server Registration" and fill out the information you want in there. To set the color, go to the connection properties tab and check off "use a custom color". Now all new connections that match that registered server exactly (exact server name and login, does not affect current connections) will have the color you specified.