Isn't that exactly the reason why Alex (the T-5000) is in Genisys? Supposedly, he is rampaging his way across the multiverse, trying to ensure Skynet's dominance in every timeline he sees.
As I recall, it was never actually established in the movie. BUT, I do remember reading an article with the writers of the movie, and they did state that the Doctor Who T-5000, which was the physical embodiment of Skynet and not just another Terminator, was indeed from an alternate timeline. I can't remember the line specifically, but Doctor Who T-5000 does say something like, "I've come a long way to find you..." He wasn't just talking about a leap though time, but also through dimensions. According to the article, anyway...
... but that would have just confused everyone even more.