Explosion is a valid target for Siren Stormtamer's ability when your opponent activates the ability. By the time the ability resolves, Explosion is no longer a valid target for the ability, so the ability fizzles for lack of legal targets. Explosion then resolves and does as much as possible, namely draw you cards.
By the time your opponent activates the ability, Explosion is targeting his Stormtamer, so Explosion is a legal target for the ability. As part of the ability activation, your opponent has to sacrifice the Stormtamer, but only after declaring targets. Sacrificing the Stormtamer as part of paying the ability activation costs has no effect on Expansion's legality as the ability's target at this point.
601.2. To cast a spell is to take it from where it is (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. Casting a spell includes proposal of the spell (rules 601.2a-d) and determination and payment of costs (rules 601.2f-h). [..]
(the rules for casting spells and activating abilities are the same as far as this question is concerned.)
When the ability resolves, it checks again that its target is still legal. Since the Stormtamer is no longer on the battlefield, Explosion no longer targets your opponent or a creature he controls. Therefore, Explosion is no longer a legal target for the Stormtamer's ability, and the ability fizzles.
- Resolving Spells and Abilities
608.2b If the spell or ability specifies targets, it checks whether the targets are still legal. [..] If all its targets, for every instance of the word "target," are now illegal, the spell or ability doesn't resolve. It's removed from the stack and, if it's a spell, put into its owner's graveyard.
Explosion can then resolve because it wasn't countered and still has a legal target; it will do as much as possible with the remaining target (yourself), so it will draw you cards.