That is a toxic Pencil Cactus, Milkbush Latin: Euphorbia tirucalli to the right in your picture towering above your plumeria. It appears the cactus has a lot of new green growth bringing it up to the roofline. The Wikipedia link en.wikipedia.org/wiki/Euphorbia_tirucalli has a picture of the flower buds ironically appear similar to your new growth on the plumeria. Since the cactus has a highly toxic latex type sap, I wonder if it is affecting the plumeria's new growth - perhaps causing "tumors" or genetic changes? The link has a paragraph about the cancer type growths. If you stand back and observe your entire plumeria most of the odd growth is towards the cactus and the last of the "normal" looking plumeria growth is furthest away from the cactus.
The growth under the plumeria may be minor but clearing that out to give good airflow might be helpful. Similarly, black spot on roses is deterred by creating good airflow with strategic pruning. I am NOT suggesting pruning the plumeria. Increasing the airflow below the plummie helps avoid fungus and bacteria growth because water will not linger as much.
