Part of Khan's work with Section 31 was to come up with technology that protected the warp core.
As for the rest of Vengeance' crew, two words:
Oddly, all of them were from New York city.
TOS style warp cores didn't go pop every time someone sneezed at them No rolling on a dropping blast door for Scotty; just fix the damn engine and move on with your day.
There was a definite lack of quality in the 24th century warp cores. Damn things were threatening to blow up all the time.
TOS engines were more like muscle cars: Something breaks, you grab a toolkit, pop the hood, fix it while downing a beer.
TNG engines: Is like more modern cars. Something breaks, you might be able to fix it, more likely you just going to fuck something up that's more expensive to fix and the engine will blow on you going down the road.