At a certain point, Skynet uploaded itself into a T-5000 Terminator and infiltrated John Connor's Tech-Com unit, leaving its core in Colorado as a decoy.
Alex then participated in Operation Chrono; after the control center in Colorado was destroyed, Alex attacked John Connor in the Time Displacement Chamber when Connor was seeing Kyle Reese off. While turning John Connor into a T-3000 Infiltrator, Alex revealed that he was Skynet itself and killed the other Tech-Com members who were present.
The physical design of "Alex", likely the last robotic unit constructed by Skynet before its network core was taken offline by Tech-Com, seems to have been brought back to 2010s by John Connor and used as holographic avatar by Genisys.
Prior to the film's release, Matt Smith's role was kept entirely secret other than the fact that he was playing someone with a strong connection to John Connor. In several sources, including Entertainment Weekly, Alex is called "The Secret" and referred as a "close ally" of John Connor. Ironically, this is true in someway as Alex transforms John into his own herald to ensure its own existence.
Despite Alex's depiction in the film Terminator Genisys, executive producer Laeta Kalogridis suggests that Alex could be Skynet's counterpart from another timeline based on his line "I’ve come a very long way to stop you." — however, it can be simply just a joke in reference to Matt Smith's portrayal of "The Doctor" from the television series Doctor Who. In addition, Alex referred to the machine army that had been disabled as "slaves", and confirmed that it was the consciousness of Skynet itself, and not just another puppet. Further explanation was never given, as there is no planned sequel by far.