ok so I've never EV trained before

I decided to ev train this little guy with horde battle and super training, got 252 SpA, 252 Spe, 6 HP and it says it's a fully trained pokemon

the only thing that bothers me is that it's still level 20. For the other 80 levels I can train however I want correct? Rare candies, battling mons that give incorrect EVs etc?

sorry if this is a dumb question, i just want to make sure before i mess up it's spread or something