Spock actually advises Kirk to strike first in Balance of Terror based on the probability that the Romulans are an offshoot of the Vulcans from a more violent past.
He's a bit more circumspect than that. He first says that Vulcan had a violent colonization period in the past, because Vulcans are violent by nature. He then says "if
Romulans retain this martial philosophy...". The use of "retain" seems to mean that Spock acknowledges the Romulans are descendants of Vulcans, something confirmed in many other places later on. But nothing indicates that retention of violence would have been the reason Romulans departed Vulcan. Indeed, Spock's reference to "colonization period" may refer to interstellar colonization performed by violent Vulcans, long before a rift developed between them and the Romulans.