Nothing anyone has done so far in this new timeline will stop that star from exploding
How do we know? A tiny drop of red matter would suffice, apparently - and Nero spent several hours with the red matter before choosing to destroy Vulcan with it.
Among the things we know he did in that time was the supposed destruction of 47 Klingon warships, indeed something better achieved with a WMD than without. But he also tells Pike "I prevented genocide!" with enough volume and saliva to make it sound fairly convincing. So, considering that his ship came out of the timehole right next to a big red star that had Klingons nearby (as per the walla aboard the Kelvin
in the opening moments), and that it had entered the timehole at a location where Spock had stopped an exploding star... Might that big red star not have been the one that would eventually explode and devour Romulus? A good reason for Nero to go challenge some Klingons and play around with his newly acquired supply of red matter!