Correct, this page is wrong. Seed of Flame is a "when... you can..."-effect, meaning the "when"-condition has to be the LAST thing to happen for its effect to work. When you use Fragrance Storm, the last thing to happen is that you draw a card, so Seed of Flame misses the timing.
Actually, it seems I was partially wrong. The destruction and the drawing actually happen at the same time, so it won't miss the timing. The problem is if that draw nets you a Plant-Type: if you show it for the extra draw, THEN you will miss the timing. However, that's optional, so if you decline the extra draw, you can still use Seed of Flame or Botanical Girl.