The wall wart transforms the power from 120v to 12v so the 120v is exactly what is appropriate when combined with the transformer.
Almost all products that use low voltage just draw as much power as is necessary to make them work. So, if you have a 12v 500ma product, and a 12v 1500ma transformer, you don't damage the product that only draws 500ma, you just have extra power left over. In your situation, you won't blow up your product because you have some extra ma left over - as long as you are feeding within the low voltage specs of the products you are trying to turn on your are fine.
12 volt output should always be constant, not pulsed to 12v triggered products. If it was a pulse that turned on the surge supressor and an identical pulse turned the surge supressor off - then how would the trigger know if it was on or off? Instead, when 12 volts exists, the supressor is on, when 12 volt doesn't exist, the surge supressor is off. There is no middle ground where it 'may be' on or it 'may be' off.