The black (from what I can see in the photos) appears to be sooty mold, which is often a consequence of aphid or scale attacks. It's more difficult to get rid of than the aphids themselves are; less difficult than the scale insects can be.
I had an outdoor podocarpus that was so infested by both scale and sooty mold several years ago that it had to be removed. The location was poor, both from a sun and an air-circulation viewpoint.
Because this plant is indoors, I would suggest very conservative treatment. Because the plant is relatively small, the conservative treatment shouldn't take forever...
According to Ellis & Bradley's 1992 Organic Gardener's Handbook of Natural Insect & Disease Control, "[Sooty mold] lives on the honeydew excreted by aphids, mealybugs, and scales. Treat the plant for the insect infestation. Then clean the foliage with warm soapy water and rinse."
You've treated--successfully!--for insects. Rather than subject the entire plant to soap again, why not try Q-tips or other gentle cotton swaps and wipe the sooty mold off of the leaves, top and bottom? If the insects are truly gone--and their eggs as well--this will improve the ability of the plant's leaves to transpire.
It will also have the benefit of not disturbing the soil.