Storm is a keyword ability that first appeared in Scourge and made a return visit in Time Spiral block. Storm is also a triggered ability that triggers when a spell with storm is cast. This trigger will go on the stack on top of the spell itself and it will resolve first. When this trigger resolves a copy of the storm spell is put on the stack for each spell that was cast before the storm spell. Then each of these copies and the original spell will resolve.

The storm ability only counts spells that are cast. It does not count when copies of spells are put on the stack. For example, if a Lightning Bolt is played, and it is copied by Reverberate, only two spells have been cast. The copy of Lightning Bolt that was created by Reverberate will not be counted. For this reason a storm ability will not count the copies made by another storm ability.

The storm trigger on the stack is independent of the storm spell. So countering the initial spell will not prevent the copies from going on the stack. These copies can be prevented from being put on the stack it the trigger is countered, but you’d need something like Stifle to do that. The other way to counter storm copies is to counter them individually.