"The wasted spark system is an ignition system used with some four-stroke cycle internal combustion engines. In a wasted spark system, the spark plugs fire in pairs even though one is on its compression stroke and one is on its exhaust stroke. The extra spark on the exhaust stroke has no effect and is thus "wasted". This design halves the number of components in a typical ignition system, while the extra spark, against much reduced dielectric resistance, barely impacts on the lifespan of modern ignition components."
That example is for a 2cyl engine, but the principle is the same. The spark plug fires on both power and exhaust stroke, but the firing on exhaust doesn't matter. As long as it is actually firing once at the right time in the stroke and is getting fuel and air, the bike should run (but perhaps poorly depending on other issues...)
Is it literally sparking "constantly" ?? It should not fire on the intake stroke which might be your sputtering issue.
Did you have the rotor off? Are you sure the "pulser coil" (trigger as you call it) checks out spec wise?
Keep feeding us info and we can help you figure this out. Don't get too discouraged