I have follow the linked tutorial but I still get a login prompt pictured below. How do I get thi...

@rw.eipi

There's a variety of scenarios that could result in the behavior you experienced. As the message says you must have been signed into Eikon platform on another machine when you tried signing in on this one. Apart from being logged into Eikon on another machine you'd get this prompt if you've signed into Eikon Web and then you try to launch Eikon desktop or sign in using Eikon Excel.
I don't think the issue is specific to using Synchronization Manager in Excel. I'm fairly confident you can reproduce the same warning and sign in prompt pop-up if you follow the exact replication steps you followed before, but instead of opening SynchroManager.xlsm and clicking Login Programmatically you click the Sign In button in Excel ribbon under the Thomson Reuters tab.
If indeed you reproduce the same behavior and you'd like to get an explanation for why it happens, I suggest you reach out to Refinitiv Helpdesk by either calling the Helpdesk number in your country or by using Contact Us capability in your Eikon application.