Hi, Sheila. For convenience, WikiTree "remembers" for a period of time that your device (computer, tablet) is authorized for your account. That's why you only seldom have to log-in for a new session if you didn't expressly log-out of the last one.
I suspect what's happening is that, when you click on a WikiTree link from GEDmatch, your device is being automatically logged into WikiTree and you see the compact tree and all related profile information as yourself, not as someone else would.
Easy way to test. Go to GEDmatch and locate one of those WikiLinks to one of your testers and click it. If, in the top right-hand corner of the window in WikiTree you see the usual pulldown menu for "My WikiTree," then you've been automatically logged in under your personal account. If you expressly log-out from WikiTree and then go try GEDmatch, I suspect you'll see what you expect the public to see based on your privacy settings.