Runaway Steam-kin rules question.

Ok, the situation is thus.

[[Runaway Steam-Kin]] is out with 2 counters on it. I cast a red spell (Doesn't matter what one). In response, my apponent casts an instant spell to kill my Steam-Kin (Again, spell doesn't matter for this example)

Here is the question. Do I now have enough counters on my Kin so I can drain it for floating mana to use after everything has resolved?

The card errata reads : "Runaway Steam-Kin’s triggered ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered."

This seams to suggest that the Kin gets the counter the moment the red spell goes onto the stack.

Yes? No? Maybe? Stop eating lead paint chips?