"Second Romulan War"?
The first one was so tasty, they came back for seconds.
In all seriousness, it's sort of a reference to Alan Dean Fosters' "Balance of Terror" novelization; that's the phrase he uses to refer to the Romulan incursion and Enterprise's interception. I include it here because (aside from the fact that I think it sounds cool) there are multiple descriptions of the Earth-Romulan War -- from the ENT/Novelverse, from TNG, from the TOS description, from other novels before ENT came out -- and they largely contradict each other. I realized that it can be explained nicely if Spock was actually referring to the Earth-Romulan Wars
, as a series of conflicts of various size and intensity that began a century ago and never completely ended. Only the first was even a declared war, the others are "wars" that involved different Romulan sub-nations/colonies fighting with different Federation members/colonies at different times using different weapons and technology. This way you wouldn't have to reconcile contradictory depictions of the Romulan War; they're ALL accurate, they just don't always refer to the same event.
So when Spock refers to the "primitive atomic weapons and in primitive space vessels" of the era, he's mainly referring to the colonial militias and the Earth Cargo Service who wound up fighting the bulk of the Romulan force while Starfleet had its hands full defending Sol. That early debacle, more than anything else, explains Starfleet's longstanding policy of isolation against the Romulans: they've been known to come busting out from time to time and you never know when they're going to make trouble again.
What of the assumption that the divergence began with the Kelvin Incident?
It most likely did, but I make no assumptions. On the one hand, the current movie produces have ALOT of room to maneuver and could play that any way they like, even ways that will make most of us angry and confused. My goal in writing this was to leave "wiggle room" where new information could fit without too much editing.