My take on the soapy water approach.
A squirt of dish detergent in 3 to 6 ounces of water makes a fairly concentrated surfactant. Aphids naturally avoid dehydration with an outer coating of a lipid of some sort. When you mist the surfactant (diluted dish detergent) directly onto an aphid, the lipid coating is dissolved. The aphid dehydrates, and dies. There is no residual effect on subsequent aphids, but the aphids that get hit directly by the mist are dead. The detergent mist is water soluble, so it washes away in rain or morning dew. I've used this approach to manage as many as 200+ plants. It's a lot of work, since you have to inspect the upper and under surfaces of every leaf, including the auricle (the "frill" where the leaf lamina meet the stalk), and mist any aphids you discover. Under significant aphid pressure (i.e. they really hate you), you need to repeat the misting every week or so. I've never detected any detergent residual on the harvested leaf.
Plan B is to haul out a garden hose, then firmly spray (not so intensely that it bruises the leaf!) the aphids from their chosen leaves. Aphids insert their mouth parts into the lamina, to suck out goodies. Once you wash them away, 1) some have had their probosces ripped off and 2) none of those washed away have a means of crawling back onto a tobacco plant. So they die as well. As with the detergent approach, there is no residual effect on subsequent aphids, so the process may need to be repeated weekly.
Flying aphids (the aphid mothers) prefer to lay their eggs on young and tender leaf. So they often choose auricles, immature main leaf, and sucker leaf. Just keeping the plants relatively sucker-free goes a long way toward minimizing aphids, especially during the late season.
Bob