Т3-4 тут вообще не к месту, потому что Т-2 придумывалась без них)
Дичайшая или нет, но главный вопрос такой: Кайл мог попасть только в то прошлое, которое его породило. Но он прыгает в альтернативное прошлое.
Вот размышления на эту тему:
The practical problems should be evident to any fan upon seeing Genisys, the main issue being Kyle Reese’s travel from the future established in the original series, to a past that would clearly not produce that same future. Kyle mentioned to Sarah in The Terminator that the time he came from was just “one possible future” – though that wasn’t his field of expertise – but basic assumptions of time travel would state no matter how he does it, the Kyle Reese 0f 2029 could only travel back along the timeline which produced that future.
The only real explanation is that “access point” created by the death of John Connor (which granted Kyle memories of both timelines) also allowed him to leap from one to the other. It’s a leap that is unexplained for now, but the actual means by which Kyle changes timelines, like the question of who sent back Pops to protect Sarah, will form the plot of this new Terminator film series.