The key in understanding this is that there a two sets of rules that govern how long Mastermind (MM) stays in play:
1) The rules for a Duration card staying in play, and
2) The rules for a "Throne Room"-like card staying in play.
The rules for a Duration card staying in play would just keep the Mastermind out for 1 turn, after that time, it did it's job of playing another card 3 times. But the rules for "Throne Room"-like cards say that such a card playing a Duration card an additional time means they stay out as long as the Duration card does.
MM1 is played on turn X. On turn X+1 MM1 plays MM2 3 times. MM1 stays out as long as MM2, according to the rules for 2) above. Since MM2 is a Duration card that has things left to do, MM1 stays at for another turn (X+2), on which MM2 plays Smithies (no relevance for staying out) and MM3. By the same argument as above, MM2 stays in play as long as MM3 does, so is staying at least until turn (X+3), which means MM1 also stays in play until at least that turn.
So your option i) is correct.