I cannot think of a circumstance in which it would be okay to apply mulch from that tree into a food consumption environment - whether organic or not. It may or may not be just fine, but emamectin benzoate is not rated for consumption. 3 years is the period over which it is effective in treating insects. I believe the label actually labels it as effective over 2 years. At year 4, there may still be emamectin benzoate present at a dose that does not affect most insects enough to kill them. At year 5, it might still be there but at a lower amount. The point being, you need to understand too much - the half-life, the mode of effect on insects and other animals, sublethal effects on insects and other animals, the constituents that it breaks down into and their effects on the garden ecosystem - at too high a level prior to jumping in. Emamectin benzoate has only been studied for its labeled applications and application rates.
Meanwhile, you can turf up a neighbor's tree that has not been treated, turn it into mulch, and apply that to the garden and get close to the same benefits of sustainability and organic agriculture.
