When they evolve they get this massive Stat boost. What is it?
No. That stat boost is simply the Base Stat requirements giving the Pokemon a boost/decrease in the affected stat. EVs are not effected.
Nope the EVs stay the same. The reason the stats are boosted is because the evolved version of the Pokemon has better base stats. So if a Pokemon has only 28 EVs in attack, they evolve, they will still have only 28 EVs in attack.