Minions can’t have spell damage applied to them in any case. Spell damage can be thought of as an aura that buffs your hero, and Sorcerous Substitute triggers as long as this buff is in play.
In the case of Talented Arcanist, the battlecry applies a spell damage buff to your hero that disappears after a spell is played. If you play Sorcerous Substitute before you play a spell, the spell damage buff is on your hero and so the battlecry condition is met.
Mechanically I’m willing to bet this is intended, even if it seems unintuitive from the wording.