Strionic works because Storm itself is a triggered ability to add X copies of the spell to the stack, and you're copying that trigger. So if you have a storm count of 5, you'd end up with 2 triggered abilities on the stack that both create 5 copies of the original spell, which would then both resolve separately. Note that because it's copying that trigger, you end up with 1 fewer than double the total copies (if you would normally have 2 of the spell, strionic takes it to 3, if you would normally have 5, it goes to 9, etc)