Air Traffic Control is a complex entity and there many sources of information available to those that service all or any flight. The technology available to control towers will include at minimum 'situational awareness' tools be they flight strips, communications or visual aids.
The visual aids will include a geographic overlay of combined sources such as MLAT, ADS-B (out), SSR, primary radar and procedural reporting.
I have no doubt that control tower staff know precisely where each and every flight is within their control zone.
As an 'amateur' ADS-B/MLAT provider to commercial web sites, I can pretty much guarantee that ATC service units, including control towers, do not get their information from the likes of me! The only reason a control tower would have an internet connection to FR24.com etc. would be if an individual were to set it up for personal interest or the tower belonged to a private airfield.