Neem does NOT kill by contact or by residual touching. It kills by smothering, choking off the pests air supply.
You're describing exactly "kill by contact" when you say "smother". Was this just a bad choice of words?
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My comment about using soap and neem together being antithetical has to do with how oils and soaps react with each other. Soap cleans an oily dish because of its molecular structure: having one end non-polar and attracting other non-polar molecules (like oils), and the other end polar and attracting polar molecules (like water). Thus, using this law of physics, it would be logical to say that neem would be less effective with soap added.
But there could be more to it than that. As Lucy points out, soap also "eats away" at the plant surface cuticles that protect it from its harsh environment, like from drying out, for instance. It also might provide an easier path for neem penetration into the plants' systems.
Obviously, both scenarios are at play, but which is more prominent, I couldn't say. I will say that any real horticulturist will think it is silly to add soap to a horticultural oil application; however horticultural oil is strictly a contact pesticide, too, where as neem is not.