Zimone's last ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered or otherwise leaves the stack.

Since Zimone's last ability won't trigger until you've finished casting your first spell with in its mana cost each turn, the counters from that ability won't be placed on Zimone until after that spell's cost has been determined. The counters put on Zimone from casting your first spell with in its mana cost do not reduce that same spell's cost.

If you cast your first spell with in its mana cost during a turn before Zimone is on the battlefield, casting another spell with in its mana cost later in the turn won't cause her last ability to trigger. That spell also won't have the cost reduction from Zimone's first ability.