ORIGINAL: AKar
It is not like a positive ID established by linking the military ground control picture to the civilian air traffic control's one is always immediately updated to the airborne interceptor, and correlated with whatever the pilot of that might see on his systems.
In many countries including the United States, the civilian air traffic control and military ground control pictures are interlinked, and in many cases the same thing as many GCI/EW radars do double duty as air traffic control radars. Military IFF works in multiple modes. Civilian transponders only squawk on Mode 3. That does not mean that the military IFF needs to be interlinked with the civilian picture to interrogate civilian transponders.
Of course, only lately we have been going into that direction with all the networking - if functional. In CMO, the color of the HAFU is changed automatically - in reality, there is somebody having to make that decision on one-to-one basis.
That's actually a setting. You can uncheck "collective responsibility" and declare targets hostile individually if you choose. If the scenario is any good, though, there will probably be more going on than a single person can handle adequately. The networking has been going on for a while. Datalinks have been a thing for decades now in the West, in the form of Link 11. It's only grown and become more automated since then. Voice radio traffic is a network as well. That's been common since WWII. The real advances have been in things like bandwidth, data fusion, and cockpit displays that allow one to make better use of the information you're receiving more quickly and build a more accurate mental picture.