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!
I don't believe Nero had the red matter until he captured Spock, and he only got Spock recently before he imploded Vulcan into a black hole, if he imploded a star, that would have attracted the attention of Star Fleet and would have ruined his surprise when he attacked Vulcan. A star big enough to go supernova is a very significant star to suddenly disappear into a black hole for no reason, the type of stars that go supernova are at least 10 solar masses, they have iron cores when they stop fusing light elements, and since fusing iron into heavier elements costs energy rather than releasing it, a star such as this collapses into a neutron star as the stars outer layers rebound against it and explode into a tremendous explosion. This star would have had to have been fairly close to Romulus to destroy the planet when it exploded, for other planets further away, you have ozone destruction and possible EMP radiation frying circuits causing massive planet wide blackouts and so forth for any planet within 50 light years of the explosion.