I like that link. It explains how Neem Oil works. The unfortunate thing is that it doesn't wotk on aphids, which is what I see from time to time.
Insects
Whiteflies, mealy bugs, armyworms, hornworms, leafhoppers, bagworms, leafminers, psyllids, fruit flies, loopers, budworms, beetles (including Japanese beetles), aphids, scales, caterpillars, midges, budworms and mites (including spider mites).
However, this does not work for all insect species. The neem ingredients accumulate in the tissues deeper inside the plant. The phloem, the outermost layer, contains hardly any. A tiny aphid feeds from the phloem, it can not penetrate deep enough to get a dose of neem. But any leaf hoppers, grass hoppers or similar chomping insects will be incapacitated quickly.
People eat neem leaves to cleanse the blood, stimulate the liver, and boost the immune system. So we certainly don't need to worry about a bit of neem inside our lettuce leaves. To me this is a much more attractive option than having poisonous foulicides build up in my garden.
Neem oil suffocates insects
Many gardeners use white oil (plain mineral oil) or even olive oil to combat soft bodied insects like aphids, thrips or whitefly. The oil coats the bugs and they suffocate. Neem oil insecticide does that as well. But it's more like a little bonus on top of everything else it does.