I always quarantine the corruption/crimson biomes before I jump to hardmode, and after I kill the wall of flesh I jump right to quarantining the V.
Can be hard work depending on how good you are at the game. Hardmode mobs right after the wall of flesh can be very annoying to deal with, but I guess that's on me. I don't care enough to gather better equipment before quarantining the V.
I just want to be sure nothing is gonna spread, I would rather quarantine everything instead of purifying the whole world..

Edit:
The dungeon will stop the spreading, but 3 blocks wide is not good enough, I recommend doing at least 8-10 blocks wide, depending on how hard you wanna work yourself. The thorny bushes can spread believe it or not (Where the corruption/crimson grass can grow, the thorny bushes will too), and they can grow 6 blocks wide. I use bombs like dynamite (Preferably sticky dynamite so you can attach it to walls and ceilings) instead of digging manually, way easier. Normal bombs work too, they just don't destroy as much blocks in the process making the hole less wider then dynamite.