Wrong. The events in the movie take place in 93 while John is only 9 not 12.
Rewatch the part after they break Sarah out of the mental institution and stop at the gas station during the daytime, shortly after John teaches the T800 how to smile (directors cut). They get into the car and Sarah asks him to explain to her how Skynet gets built. Arnold proceeds to explain to her that the man most responsible in Miles Bennet Dyson. (I'm actually watching the movie as I type this so I know my info is on point). Anyways, he explains that "in a few months" (from the current point in time in the film) Miles will create the chip, then 3 years later (1996) Cyberdyne will become the worlds largest supply of Military Computer Systems and that all stealth bombers are installed with Cyberdyne computers becoming fully unmanned. Skynet funding bill is passed and the system goes online August 4th 1997. It becomes "self aware" at 2:14 a.m. Eastern Time, August 29th, 1997. Cyberdyne tries to pull the plug and in self defense, Skynet sets off our nukes against the targets in Russia.