By treating your trees 'systemically with Bonide' I see a couple of Bonide products that fit that description. Both have EPA Registration Numbers of 53883-205-4---which you can find on the pesticide label. The active ingredient here is imidacloprid---which is also on the label. Is that the product?

I think the primary problem here is timing; secondly, how long would a treatment last---probably not as long as you think, even if the label does say something like 'year long protection.' It would depend on when that year started.

Second question, what trees did you treat? Landscape ornamentals or fruit trees or both?

What kinds of insects are on these various trees---now? Chances are, they are or have been aphids of various kinds. These are generally cool weather insects belonging to several genera and numerous species. Some are generalists when it comes to hosts while others are host plant specific to varying degrees. They pierce the foliage or thin bark of twigs and suck large amounts of plant sap. Their liquid waste products are sprayed out of their bodies; that waste is called honeydew---which is what you're calling 'sticky and shiny.' Since honeydew contains sugars made during plant photosynthesis, it is detectable and highly attractive to bees, ants, wasps, flies and other creatures searching for food.

Aphid populations also attract natural enemies---especially ladybird beetles or ladybugs. After finding prey, they reproduce; then both adults and larvae actively feed on aphid populations. There also can be syrphid flies, lacewings and various minute parasitoids that join in, feeding on the aphids. By the time the spring winds slow down and it gets hot at the end of May and June, the aphids are essentially gone and the beneficials are dispersing elsewhere to find other sources of prey. That's biological control in action. Some situations with some trees may be worth treatment, but others may not.

When the weather cools in the fall, winged aphids of various genera and species return to their host plants. Some feed while others don't. They may lay overwintering eggs on the bark, but these won't hatch until the following spring. Applications made in the fall may have impacted some of these returning insects, but not all and they likely wouldn't affect the egg stages. However, they could impact any fall populations of biological control agents that might be overwintering on these same trees or shrubs.

If you have various scale insects on trees and shrubs, the label states to apply the product when crawlers are present.  For most scales, crawlers are present in the spring. While some scale insects have multiple hosts, others don't and their life cycles and management strategies can be different. See the photo of the black scale insects. Those orange dots on these small scales are the crawlers---very small.

If you have scales on fruit trees, there's a table or two on the label that suggest approximate times for making applications on any of the common fruit trees. That would be post-pollination time but while crawlers are present.

Another consideration here---you might look into horticultural oils as 'dormant sprays' for next year. They would be applied according to label instructions when the trees or shrubs are dormant. Oils cover whatever overwintering stages of various insects they touch, smothering them. Products like this applied in the winter or before bud break are not likely to affect nesting birds which will return early in spring.

I hope this helps? Good luck with your projects.