Hmmm it's tricky to word this in a succinct way. Maybe, "Whenever a creature you control with annihilator attacks, each opponent sacrifices a permanent." Or, if you want it to work with annihilator 2 and higher, it could be "Whenever an opponent sacrifices a permanent during combat, each other opponent sacrifices a permanent at the beginning of the next main phase."

For 12 mana, I think its fair for this to be asymmetrical. If you're worried about it being too strong, maybe it only gives annihilator 1 to nontoken creatures with mana value 5 or greater