Leveling does not directly affect a Pokemon's EVs (and therefore Super Training.) In prior generations (before V, I believe,) EVs were only calculated upon leveling, so a level 100 Pokemon could not be EV trained. Now, however, EVs are calculated after each battle (and probably between battles, in the case of Super Training.)

However, leveling via battle affects Super Training because it grants EVs based on the Pokemon fought. So leveling via rare candies won't affect super training, but leveling through battle will.

I believe that EXP Share grants EVs to all Pokemon, but can't confirm this at the moment.

Leveling does not directly affect a Pokemon's EVs (and therefore Super Training.) In prior generations (before V, I believe,) EVs were only calculated upon leveling, so a level 100 Pokemon could not be EV trained. Now, however, EVs are calculated after each battle (and probably between battles, in the case of Super Training.)

However, leveling via battle affects Super Training because it grants EVs based on the Pokemon fought. So leveling via rare candies won't affect super training, but leveling through battle will.

I believe that EXP Share grants EVs to all Pokemon—confirmed by UnderscoreZero in the comments.