Negating the activation of a card or effect and destroying that card are not the same thing; as such, even if a card is Chained to the activation of a card or effect to destroy that card, its effect may still resolve.
Chaining "Raigeki Break" to the activation of a monster effect such as that of "Number 11: Big Eye" will destroy the monster, but its effect will still resolve (so "Number 11: Big Eye" will still allow the player to take control of one of their opponent's monsters).
Spells and Traps
Chaining "Mystical Space Typhoon" or "Dust Tornado" to a Normal Spell, Normal Trap Card, Quick-Play Spell Card or Ritual Spell Card has no effect on gameplay, as it does not negate the card's effect. If such a card is activated and is destroyed by a card, its effect still resolves and the card used to destroy it is essentially wasted.
- Step 1: Player A activates "Raigeki".
- Step 2: Player B Chains "Imperial Order" to negate the effect of "Raigeki".
- Step 3: Player A Chains "Mystical Space Typhoon" (or "Dust Tornado") to destroy "Imperial Order".
The Chain resolves in reverse.
- Step 3 resolves first. "Mystical Space Typhoon" destroys "Imperial Order".
- Step 2 would resolve next. "Imperial Order" has been destroyed though and its effect disappears.
- Step 1 resolves last. "Raigeki's" effect activates as normal.
For exactly the same reason, if you Chain "Mystical Space Typhoon" to "The Eye of Truth", "Future Fusion", "Premature Burial", or "Call of the Haunted", the effects from those cards do not resolve and it resolves with no effect.
Field Spells, Continuous Spells and Continuous Traps
Continuous, Field, or Equip Spell Card, or Continuous Trap Card do not work in the same manner as other spells and traps. The continuous effects and other effects on these cards that are supposed to be applied during the resolving of these cards will not apply if these cards are removed from the field before resolving. They still resolve, but resolve with no effect. Essentially, these effects for cards that activate on the field can be thought of as having the condition "You must control this face-up card to activate and to resolve this effect." Since this applies to all of them, it's just not included. However, other effects on these cards (such as separate Trigger-like effects) will still behave in their typical way.
If "Macro Cosmos" is activated, and your opponent Chains "Mystical Space Typhoon" to its activation, then "Macro Cosmos" is destroyed, and it resolves with no effect; you do not get to Special Summon a "Helios - The Primordial Sun". The same case goes to "Fire Formation - Tenki", If it gets destroyed by "Mystical Space Typhoon" when it's activated, you do not get to add 1 Beast-Warrior-Type Monster.
However if you you were to activate "Mystical Space Typhoon" to target a face down "Macro Cosmos", "Macro Cosmos" could be activated and chained in response to Mystical Space Typhoon's activation. In this case, because the chain resolves backwards, "Macro Cosmos" would still be face up on the field when its effect to Special Summon a "Helios - The Primordial Sun" resolved and "Helios - The Primordial Sun" would be summoned before Mystical Space Typhoon's effect destroyed and removed "Macro Cosmos" from the field.
Note that certain effects such as Trigger-like effects are treated normally. "Geartown" will miss the timing if when it is activated (Chain Link 1) "Mystical Space Typhoon" destroys it as Chain Link 2, since the last thing to happen was it resolving (without effect), not it being destroyed; if instead its activation is negated by "Magic Jammer", then the last thing to happen was it being destroyed, so it can activate its effect.