I was thinking of using a systemic fungicide that is applied as a soil drench around the plumeria trees.
The plumeria is on the perimeter of the property so it will be hard to spray it without spraying into my neighbors yard and my water pressure is very poor, otherwise, I would just jet it off with water. Plumerias have a small shallow root system and I have not had encountered any roots from the plumeria in all of the years I have gardened here so I think that I don't have to worry about root translocation, but mostly from possible runoff.
The sooty mold is probably from the severe white fly problems this year. I don't really see any now, but it could have been there earlier. I had been blasting the citrus, and peppers and hibiscus with water earlier this year to keep them off of them. And the corn did its' job of attracting the purple ladybugs that finally got control of the problem. I don't usually look at the plumeria leaves until they drop. The leaves will fall off and if I keep picking them up it should be less of a problem next year. the sooty mold is also on the branches. It could have just grown from the fallen sap like they did on the citrus and ti. It is unusual for ti to get sooty mold. The problem is the plumeria rust which really weakens the trees and makes them more susceptible. The fungicide is more to control the rust than anything else. I will put out ant bait under the trees and that will keep aphids and scale off but not white flies.
Happy gardening in Hawaii. Gardens are where people grow.