I'm having a hard time understanding this

Perhaps if you can tell us what criteria you use to choose to believe marketing text, we can explain marketing text.

Dan

Cap'n Jack's active ingredient is Spinosad. Its mode of action requires ingestion, meaning chewing and munching. Piercing/sucking insects aren't much affected. I'd opt for not using this product if control of aphids is your aim. They don't ingest leaves, they suck plant juices (sap). Spinosad is not absorbed into the vascular system, therefore can't infect insects that feed that way. Or at least, the control will be extremely haphazard.

That's why aphids aren't listed on the label. The manufacturers don't want complaints or lawsuits related to the ineffectiveness of their product.

Do a bit of reading up on Spinosad and you'll understand more than what I've tried to explain.

If any product with Spinosad as the active ingrediant is being looked at for use be aware this stuff is known to be highly toxic to bees and many forms of aquatic life with a lower level of toxicity to birds, but enough toxicity to be of concern.

"Highly toxic" is hyperbole. Aquatic life and birds is also an overstatement. Spinosad degrades rapidly in soil. It is toxic to bees if sprayed while they are foraging: so, in the middle of the day, onto/near flowers. Applied to leaves, evening or early morning, it has little to no effect on bees.

Depending where you are in the country, you might decide you want zero impact on honeybees, as east coast populations have been decimated by mites and who knows what else. In the part of California I'm in, they are vigorous, in little danger, and I'm comfortable applying spinosad to leaves at times they aren't active.

http://www.ncbi.nlm.nih.gov/pubmed/15366583 

"Spinosad is practically non-toxic to slightly toxic to birds, based on studies with bobwhite quail and mallard ducks. " http://npic.orst.edu/factsheets/spinosadgen.html 

Dow agrosciences of all companies has a comprehensive PDF on many studies of this. Simply, don't spray on flowering plants during the day.

I have two containers of adult Mexican beetles and their larve. One i spayed with Capt Jacks. 4 hours later they are all alive? I don't think this product works?

Doesn't sound like you are using the product correctly. For the product to be effective, the insect pests must ingest treated foliage. You cannot just spray them directly and hope it will work.

I had applied at least 2 to 3 times. Then I starting to manually remove. Yesterday I caputured about 4 adults and 15 larve.