This question is very close to this: How does Super Training work?, but I would like to know one thing in particular: Does leveling your pokemon also reduce the amount of super training one can complete?
I would assume that EV training does, but using the newly-upgraded EXP share (that now affects your entire team), could I accidentally cut how much EV I can accomplish? My friend was playing for a while, and he saw that, although he hadn't done any Super Training, some of the green bar on the right had filled. I don't think he was thinking of EV impacting it (it was on one of his main fighters that he noticed this), but I would like to be sure just in case.
Best Answer
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.